{"id":9331,"date":"2022-02-20T20:10:30","date_gmt":"2022-02-20T20:10:30","guid":{"rendered":"https:\/\/10minuteschool.com\/content\/?p=9331"},"modified":"2022-05-24T10:12:19","modified_gmt":"2022-05-24T04:12:19","slug":"logarithms-methods-of-logarithm","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/logarithms-methods-of-logarithm\/","title":{"rendered":"\u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae (Logarithms)"},"content":{"rendered":"<ul>\n<li><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\">=N<\/span><b>\u00a0 <\/b><span style=\"font-weight: 400;\">a&gt;0.\u00a0a\u22601<\/span><b> \u09b9\u09b2\u09c7, <\/b><span style=\"font-weight: 400;\">x=<\/span><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\">N<\/span><b> \u0995\u09c7 <\/b><span style=\"font-weight: 400;\">N<\/span><b> \u098f\u09b0 <\/b><span style=\"font-weight: 400;\">a<\/span><b> \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf\u0995 \u09b2\u0997 \u09ac\u09b2\u09be \u09b9\u09df\u0964<\/b><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae\u0995\u09c7 \u09b8\u0982\u0995\u09cd\u09b7\u09c7\u09aa\u09c7 \u09b2\u0997<\/span><span style=\"font-weight: 400;\"> (log) <\/span><span style=\"font-weight: 400;\">\u09b2\u09c7\u0996\u09be \u09b9\u09df\u0964<\/span><\/li>\n<\/ul>\n<h2><b>\u09b2\u0997 \u09b2\u09c7\u0996\u09be\u09b0 \u09a8\u09bf\u09df\u09ae-<\/b><\/h2>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u09b8\u09c2\u099a\u0995\u09c0\u09df \u098f\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09b9\u09b2\u09cb \u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae (Logarithms)<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u09b2\u0997\u09c7\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09b9\u09b2\u09cb \u09b8\u09c2\u099a\u0995\u09c0\u09df<\/span><\/li>\n<\/ul>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">y=<\/span><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\"> \u099c\u09be\u09df\u0997\u09be \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8 \u0995\u09b0\u09b2\u09c7 <\/span><span style=\"font-weight: 400;\">\u2192x=<\/span><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\">y<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u00a0log<\/span><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\">MNP\u2026<\/span><span style=\"font-weight: 400;\">=\u00a0<\/span><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\">M+<\/span><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\">N+<\/span><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\">P+\u2026<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">\u0995\u09bf\u09a8\u09cd\u09a4\u09c1, <\/span><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">M\u00b1N<\/span><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\">M\u00b1<\/span><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\">N<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">M<\/span><span style=\"font-weight: 400;\">N<\/span><span style=\"font-weight: 400;\">=M-N<\/span><span style=\"font-weight: 400;\"> \u00a0 <\/span><\/li>\n<\/ul>\n<h3><b>\u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u09ac\u09c8\u099c\u09cd\u099e\u09be\u09a8\u09bf\u0995 \u09b0\u09c2\u09aa <\/b><b>(Scientific F0rms of Numbers)<\/b><\/h3>\n<p><b>\u09b9\u09bf\u09b8\u09c7\u09ac\u09c7\u09b0 \u09b8\u09c1\u09ac\u09bf\u09a7\u09be\u09b0\u09cd\u09a5\u09c7 \u0985\u09a8\u09c7\u0995 \u09ac\u09dc \u09ac\u09be \u0985\u09a8\u09c7\u0995 \u099b\u09cb\u099f \u09b8\u0982\u0996\u09cd\u09af\u09be\u0995\u09c7 <\/b><span style=\"font-weight: 400;\">a\u00d7<\/span><span style=\"font-weight: 400;\">10<\/span><span style=\"font-weight: 400;\">n<\/span><b> \u0986\u0995\u09be\u09b0\u09c7 \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09be \u09b9\u09df<\/b><span style=\"font-weight: 400;\">\u0964 \u09af\u09c7\u0996\u09be\u09a8\u09c7 <\/span><span style=\"font-weight: 400;\">1\u2264a&lt;10<\/span><span style=\"font-weight: 400;\"> \u098f\u09ac\u0982 <\/span><span style=\"font-weight: 400;\">n\u2208Z<\/span><span style=\"font-weight: 400;\"> \u0964 \u0995\u09cb\u09a8 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 <\/span><span style=\"font-weight: 400;\">a\u00d7<\/span><span style=\"font-weight: 400;\">10<\/span><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\"> \u09b0\u09c2\u09aa\u0995\u09c7 \u09ac\u09b2\u09be \u09b9\u09df \u09b8\u0982\u0996\u09cd\u09af\u09be\u099f\u09bf\u09b0 \u09ac\u09c8\u099c\u09cd\u099e\u09be\u09a8\u09bf\u0995 \u09ac\u09be \u0986\u09a6\u09b0\u09cd\u09b6 \u09b0\u09c2\u09aa\u0964<\/span><\/p>\n<p><b>Note:-<\/b><\/p>\n<p><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\">b\u2192a&gt;0;a\u22601;b&gt;0;b\u22601<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">=logx<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">=log<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u098f\u09b0<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u098f\u09b0<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u09ae\u09be\u09a8<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">(0,\u00a0\u221e\u00a0)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\"> \u09ab\u09be\u0982\u09b6\u09a8\u09c7\u09b0 \u09a1\u09cb\u09ae\u09c7\u09a8 , <\/span><span style=\"font-weight: 400;\">x=(0,\u00a0\u221e)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u2234<\/span><span style=\"font-weight: 400;\"> \u09ac\u09c8\u099c\u09cd\u099e\u09be\u09a8\u09bf\u0995 \u09b0\u09c2\u09aa : <\/span><span style=\"font-weight: 400;\">a\u00d7<\/span><span style=\"font-weight: 400;\">10<\/span><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\">\u00a0(1\u2264a&lt;10\u00a0<\/span><span style=\"font-weight: 400;\"> \u098f\u09ac\u0982 <\/span><span style=\"font-weight: 400;\">n\u2208<\/span><span style=\"font-weight: 400;\">Z<\/span><span style=\"font-weight: 400;\">)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\"> \u098f\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 <\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\"> \u098f\u09b0 \u09ae\u09be\u09a8 <\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\"> \u09a5\u09c7\u0995\u09c7 \u09ac\u09dc\u0964 \u098f\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 <\/span><span style=\"font-weight: 400;\">(0,\u00a0\u221e\u00a0)<\/span><span style=\"font-weight: 400;\"> \u09af\u09c7\u0996\u09be\u09a8\u09c7 <\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\"> \u098f\u09b0 \u09a1\u09cb\u09ae\u09c7\u09a8 <\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\"> \u09a5\u09c7\u0995\u09c7 \u09ac\u09dc\u0964<\/span><\/p>\n<p>&nbsp;<\/p>\n<h2><b>\u09b8\u09c2\u099a\u0995 \u09b9\u09a4\u09c7 \u09b2\u0997\u09c7\u09b0 \u0995\u09bf\u099b\u09c1 \u09ae\u09be\u09a7\u09cd\u09af\u09ae \u09a8\u09bf\u09b0\u09cd\u09a3\u09df<\/b><\/h2>\n<table>\n<tbody>\n<tr>\n<td><b>\u09b8\u09c2\u099a\u0995\u09c7\u09b0 \u09ae\u09be\u09a7\u09cd\u09af\u09ae\u09c7<\/b><\/td>\n<td><b>\u09b2\u0997\u09c7\u09b0 \u09ae\u09be\u09a7\u09cd\u09af\u09ae\u09c7<\/b><\/td>\n<td><b>\u09b8\u09c2\u099a\u0995\u09c7\u09b0 \u09ae\u09be\u09a7\u09cd\u09af\u09ae\u09c7<\/b><\/td>\n<td><b>\u09b2\u0997\u09c7\u09b0 \u09ae\u09be\u09a7\u09cd\u09af\u09ae\u09c7<\/b><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">=100<\/span><\/td>\n<td><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">10<\/span><span style=\"font-weight: 400;\">100=2<\/span><\/td>\n<td><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\">=1<\/span><\/td>\n<td><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">r<\/span><span style=\"font-weight: 400;\">1=0<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">3<\/span><span style=\"font-weight: 400;\">-2<\/span><span style=\"font-weight: 400;\">=<\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">9<\/span><\/td>\n<td><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">3<\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">9<\/span><span style=\"font-weight: 400;\">\u00a0=-2<\/span><\/td>\n<td><span style=\"font-weight: 400;\">e<\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\">=1<\/span><\/td>\n<td><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">e<\/span><span style=\"font-weight: 400;\">1=0<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">=<\/span><span style=\"font-weight: 400;\">2<\/span><\/td>\n<td><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">=<\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">2<\/span><\/td>\n<td><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\">=1<\/span><\/td>\n<td><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\">1=0<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">&#8211;<\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">=<\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">2<\/span><\/td>\n<td><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">=-<\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">2<\/span><\/td>\n<td><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">=10<\/span><\/td>\n<td><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">10<\/span><span style=\"font-weight: 400;\">10=1<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<h4><b>\u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09c7\u099f\u09b0\u09c7\u09b0<\/b><b>\u00a0<\/b><b>\u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7<\/b><b>\u00a0<\/b><b>\u09ac\u09c8\u099c\u09cd\u099e\u09be\u09a8\u09bf\u0995<\/b><b>\u00a0<\/b><b>\u09b0\u09c2\u09aa (Scientific form of Logarithm Using Calculator)-<\/b><\/h4>\n<p><span style=\"font-weight: 400;\">Digit<\/span><span style=\"font-weight: 400;\">\u00a0=\u00a0\u2192<\/span><span style=\"font-weight: 400;\">ENG<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0985\u09a8\u09c7\u0995 \u09ac\u09dc \u09ac\u09be \u099b\u09cb\u099f \u09b8\u0982\u0996\u09cd\u09af\u09be\u0995\u09c7 <\/span><span style=\"font-weight: 400;\">a\u00d71<\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\"> \u0986\u0995\u09be\u09b0\u09c7 \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09be \u09b9\u09df\u0964 \u098f\u0996\u09be\u09a8\u09c7 <\/span><span style=\"font-weight: 400;\">1\u2264a&lt;10<\/span><span style=\"font-weight: 400;\"> \u098f\u09ac\u0982 <\/span><span style=\"font-weight: 400;\">n\u2208<\/span><span style=\"font-weight: 400;\">Z<\/span><span style=\"font-weight: 400;\"> \u0964 \u0995\u09cb\u09a8 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 <\/span><span style=\"font-weight: 400;\">a\u00d71<\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\"> \u09b0\u09c2\u09aa\u0995\u09c7 \u09ac\u09b2\u09be \u09b9\u09df \u0990 \u09b8\u0982\u0996\u09cd\u09af\u09be\u099f\u09bf\u09b0 \u09ac\u09c8\u099c\u09cd\u099e\u09be\u09a8\u09bf\u0995 \u09b0\u09c2\u09aa\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae\u09c7\u09b0 \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf \u0989\u09b2\u09cd\u09b2\u09c7\u0996 \u09a8\u09be \u09a5\u09be\u0995\u09b2\u09c7 \u09b0\u09be\u09b6\u09bf\u09b0 \u09ac\u09c0\u099c\u0997\u09be\u09a3\u09bf\u09a4\u09c0\u09df \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 <\/span><span style=\"font-weight: 400;\">e<\/span><span style=\"font-weight: 400;\"> \u0995\u09c7 \u098f\u09ac\u0982 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u098f\u0995\u0995\u0995\u09c7 \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf \u09b9\u09bf\u09b8\u09c7\u09ac\u09c7 \u09a7\u09b0\u09be \u09b9\u09df\u0964 \u09b2\u0997 \u09b8\u09be\u09b0\u09a3\u09bf\u09a4\u09c7 \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf <\/span><span style=\"font-weight: 400;\">10<\/span><span style=\"font-weight: 400;\"> \u09a7\u09b0\u09a4\u09c7 \u09b9\u09df\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\"> \u098f\u09b0 \u09ae\u09be\u09a8 \u0995\u09cb\u09a8 \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995 \u09b8\u0982\u0996\u09cd\u09af\u09be \u09a8\u09df, \u098f\u09b0 \u09ae\u09be\u09a8 <\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\"> \u09a5\u09c7\u0995\u09c7 \u09ac\u09dc\u0964<\/span><\/p>\n<h3><b>\u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae \u09aa\u09a6\u09cd\u09a7\u09a4\u09bf <\/b><b>(Logarithmic Method)<\/b><\/h3>\n<p><span style=\"font-weight: 400;\"> \u09b2\u0997 \u09aa\u09cd\u09b0\u09a7\u09be\u09a8\u09a4 \u09a6\u09c1\u0987 \u09aa\u09cd\u09b0\u0995\u09be\u09b0\u0964 \u09af\u09a5\u09be:-<\/span><\/p>\n<ol>\n<li><span style=\"font-weight: 400;\">i)<\/span><span style=\"font-weight: 400;\"> \u09b8\u09cd\u09ac\u09be\u09ad\u09be\u09ac\u09bf\u0995 \u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae <\/span><span style=\"font-weight: 400;\">(ln)<\/span><\/li>\n<li><span style=\"font-weight: 400;\">ii)<\/span><span style=\"font-weight: 400;\"> \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae <\/span><span style=\"font-weight: 400;\">(log)<\/span><\/li>\n<\/ol>\n<h4><b>\u09b8\u09cd\u09ac\u09be\u09ad\u09be\u09ac\u09bf\u0995 \u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae <\/b><b>(Natural Logarithm) :<\/b><b><\/b><\/h4>\n<p><span style=\"font-weight: 400;\">Calculator<\/span><span style=\"font-weight: 400;\"> \u098f <\/span><span style=\"font-weight: 400;\">AC<\/span><span style=\"font-weight: 400;\">ln\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09b8\u09cd\u0995\u099f\u09b2\u09cd\u09af\u09be\u09a8\u09cd\u09a1\u09c7\u09b0 \u0997\u09a3\u09bf\u09a4\u09ac\u09bf\u09a6 \u099c\u09a8 \u09a8\u09c7\u09aa\u09bf\u09df\u09be\u09b0 <\/span><span style=\"font-weight: 400;\">(1550-1617) <\/span><span style=\"font-weight: 400;\">\u09e7\u09ec\u09e7\u09ea \u09b8\u09be\u09b2\u09c7 <\/span><span style=\"font-weight: 400;\">e<\/span><span style=\"font-weight: 400;\"> \u0995\u09c7 \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf \u09a7\u09b0\u09c7 \u09aa\u09cd\u09b0\u09a5\u09ae \u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u09bf\u09a4 \u09ac\u0987 \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09c7\u09a8\u0964 <\/span><span style=\"font-weight: 400;\">e<\/span><span style=\"font-weight: 400;\"> \u098f\u0995\u099f\u09bf \u0985\u09ae\u09c2\u09b2\u09a6 \u09b8\u0982\u0996\u09cd\u09af\u09be, <\/span><span style=\"font-weight: 400;\">e=2.71828\u2026<\/span><span style=\"font-weight: 400;\"> \u0964 \u098f\u0995\u09c7 \u09a4\u09a4\u09cd\u09a4\u09cd\u09ac\u09c0\u09df \u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae <\/span><span style=\"font-weight: 400;\">\u2192<\/span><span style=\"font-weight: 400;\"> \u09a8\u09c7\u09aa\u09b2\u09bf\u09df\u09a8 \u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae <\/span><span style=\"font-weight: 400;\">\u2192<\/span><span style=\"font-weight: 400;\">\u00a0e<\/span><span style=\"font-weight: 400;\"> \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf\u0995 \u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae \u09ac\u09b2\u09be \u09b9\u09df\u0964 <\/span><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">e<\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\"> \u0995\u09c7 <\/span><span style=\"font-weight: 400;\">lnx<\/span><span style=\"font-weight: 400;\"> \u0986\u0995\u09be\u09b0\u09c7\u0993 \u09b2\u09c7\u0996\u09be \u09b9\u09df\u0964<\/span><\/p>\n<h4><b>\u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae <\/b><b>(Common Logarithm) :<\/b><\/h4>\n<p><span style=\"font-weight: 400;\">\u0987\u0982\u09b2\u09cd\u09af\u09be\u09a8\u09cd\u09a1\u09c7\u09b0 \u0997\u09a3\u09bf\u09a4\u09ac\u09bf\u09a6 \u09b9\u09c7\u09a8\u09b0\u09bf \u09ac\u09cd\u09b0\u09bf\u0997\u09b8 <\/span><span style=\"font-weight: 400;\">(1561-1630)<\/span><span style=\"font-weight: 400;\"> \u09e7\u09ec\u09e8\u09ea \u09b8\u09be\u09b2\u09c7 <\/span><span style=\"font-weight: 400;\">10<\/span><span style=\"font-weight: 400;\"> \u0995\u09c7 \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf \u09a7\u09b0\u09c7 \u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae\u09c7\u09b0 \u099f\u09c7\u09ac\u09bf\u09b2 \u09a4\u09c8\u09b0\u09c0 \u0995\u09b0\u09c7\u09a8\u0964 \u098f\u0995\u09c7 \u09ac\u09cd\u09b0\u09bf\u0997\u09b8 \u099f\u09c7\u09ac\u09bf\u09b2 \u09ac\u09b2\u09c7\u0964 \u098f\u0987 \u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae\u0995\u09c7 <\/span><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">10<\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\"> \u0986\u0995\u09be\u09b0\u09c7 \u09b2\u09c7\u0996\u09be \u09af\u09be\u09df\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09bf.\u09a6\u09cd\u09b0.: <\/span><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\"> \u098f \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf\u09b0 \u0995\u09a5\u09be \u0989\u09b2\u09cd\u09b2\u09c7\u0996 \u09a8\u09be \u09a5\u09be\u0995\u09b2\u09c7 \u09b0\u09be\u09b6\u09bf\u09b0 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09df \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 <\/span><span style=\"font-weight: 400;\">e<\/span><span style=\"font-weight: 400;\"> \u0995\u09c7 \u098f\u09ac\u0982 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 <\/span><span style=\"font-weight: 400;\">10<\/span><span style=\"font-weight: 400;\"> \u0995\u09c7 \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf \u09b9\u09bf\u09b8\u09c7\u09ac\u09c7 \u09a7\u09b0\u09be \u09b9\u09df\u0964 <\/span><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\"> \u09b8\u09be\u09b0\u09a3\u09bf\u09a4\u09c7 \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf <\/span><span style=\"font-weight: 400;\">10<\/span><span style=\"font-weight: 400;\"> \u09a7\u09b0\u09a4\u09c7 \u09b9\u09df\u0964\u00a0<\/span><\/p>\n<h3><b>\u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b2\u0997\u09c7\u09b0 \u09aa\u09c2\u09b0\u09cd\u09a3\u0995 <\/b><b>(Characteristics of Common Log)<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">\u098f\u0995\u099f\u09bf \u09b8\u0982\u0996\u09cd\u09af\u09be <\/span><span style=\"font-weight: 400;\">N<\/span><span style=\"font-weight: 400;\"> \u0995\u09c7 \u09ac\u09c8\u099c\u09cd\u099e\u09be\u09a8\u09bf\u0995 \u0986\u0995\u09be\u09b0\u09c7 \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n<p><span style=\"font-weight: 400;\">N=a\u00d71<\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\"> \u09af\u09c7\u0996\u09be\u09a8\u09c7 <\/span><span style=\"font-weight: 400;\">N&gt;0,\u00a01\u2264a&lt;10<\/span><span style=\"font-weight: 400;\"> \u098f\u09ac\u0982 <\/span><span style=\"font-weight: 400;\">n\u2208<\/span><span style=\"font-weight: 400;\">Z<\/span><span style=\"font-weight: 400;\"> \u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0989\u09ad\u09df \u09aa\u0995\u09cd\u09b7\u09c7 <\/span><span style=\"font-weight: 400;\">10<\/span><span style=\"font-weight: 400;\"> \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf\u0995 \u09b2\u0997 \u09a8\u09bf\u09df\u09c7 \u09aa\u09be\u0987,\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">10<\/span><span style=\"font-weight: 400;\">N=n+<\/span><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">10<\/span><span style=\"font-weight: 400;\">a<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">n<\/span><b> \u0995\u09c7 \u09ac\u09b2\u09be \u09b9\u09df <\/b><span style=\"font-weight: 400;\">logN<\/span><b> \u098f\u09b0 \u09aa\u09c2\u09b0\u09cd\u09a3\u0995\u0964<\/b><\/li>\n<\/ul>\n<table>\n<tbody>\n<tr>\n<td><span style=\"font-weight: 400;\">N<\/span><\/td>\n<td><span style=\"font-weight: 400;\">N<\/span><b> \u098f\u09b0 \u09ac\u09c8\u099c\u09cd\u099e\u09be\u09a8\u09bf\u0995 \u09b0\u09c2\u09aa<\/b><\/td>\n<td><b>\u09b8\u09c2\u099a\u0995<\/b><\/td>\n<td><b>\u09a6\u09b6\u09ae\u09bf\u0995 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u09ac\u09be\u09ae\u09c7\u09b0 \u0985\u0982\u09b6\u09c7\u09b0 \u0985\u0999\u09cd\u0995\u09b8\u0982\u0996\u09cd\u09af\u09be <\/b><span style=\"font-weight: 400;\">1<\/span><b> \u0993 <\/b><span style=\"font-weight: 400;\">2<\/span><b>\u0964 \u09a6\u09b6\u09ae\u09bf\u0995 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u0993 \u098f\u09b0 \u09aa\u09b0\u09ac\u09b0\u09cd\u09a4\u09c0 \u09b8\u09be\u09b0\u09cd\u09a5\u0995 \u0985\u0999\u09cd\u0995\u09c7\u09b0 \u09ae\u09be\u099d\u09c7 <\/b><span style=\"font-weight: 400;\">0<\/span><b> \u098f\u09b0 \u09b8\u0982\u0996\u09cd\u09af\u09be<\/b><\/td>\n<td><b>\u09aa\u09c2\u09b0\u09cd\u09a3\u0995<\/b><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">6237<\/span><\/td>\n<td><span style=\"font-weight: 400;\">6.237\u00d71<\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\">3<\/span><\/td>\n<td><span style=\"font-weight: 400;\">3<\/span><\/td>\n<td><span style=\"font-weight: 400;\">4<\/span><\/td>\n<td><span style=\"font-weight: 400;\">4-1=3<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">623.7<\/span><\/td>\n<td><span style=\"font-weight: 400;\">6.237\u00d71<\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\">2<\/span><\/td>\n<td><span style=\"font-weight: 400;\">2<\/span><\/td>\n<td><span style=\"font-weight: 400;\">3<\/span><\/td>\n<td><span style=\"font-weight: 400;\">3-1=2<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">0.6237<\/span><\/td>\n<td><span style=\"font-weight: 400;\">6.237\u00d71<\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\">-1<\/span><\/td>\n<td><span style=\"font-weight: 400;\">&#8211;<\/span><span style=\"font-weight: 400;\">1<\/span><\/td>\n<td><span style=\"font-weight: 400;\">0<\/span><\/td>\n<td><span style=\"font-weight: 400;\">-(0+1)=-1=<\/span><span style=\"font-weight: 400;\">1<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">0.06237<\/span><\/td>\n<td><span style=\"font-weight: 400;\">6.237\u00d71<\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\">-2<\/span><\/td>\n<td><span style=\"font-weight: 400;\">&#8211;<\/span><span style=\"font-weight: 400;\">2<\/span><\/td>\n<td><span style=\"font-weight: 400;\">1<\/span><\/td>\n<td><span style=\"font-weight: 400;\">&#8211;<\/span><span style=\"font-weight: 400;\">1+1<\/span><span style=\"font-weight: 400;\">=-2=<\/span><span style=\"font-weight: 400;\">2<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3><b>\u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b2\u0997\u09c7\u09b0 \u0985\u0982\u09b6\u0995 <\/b><b>(Mantissa of Common Log)<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">\u0995\u09cb\u09a8 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b2\u0997\u09c7\u09b0 \u0985\u0982\u09b6\u0995, <\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\"> \u0985\u09aa\u09c7\u0995\u09cd\u09b7\u09be \u099b\u09cb\u099f \u098f\u0995\u099f\u09bf \u0985\u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995 \u09b8\u0982\u0996\u09cd\u09af\u09be\u0964 \u098f\u099f\u09bf \u09ae\u09c2\u09b2\u09a4 \u0985\u09ae\u09c2\u09b2\u09a6 \u09b8\u0982\u0996\u09cd\u09af\u09be\u0964 \u09a4\u09ac\u09c7 \u098f\u0995\u099f\u09bf \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09a6\u09b6\u09ae\u09bf\u0995 \u09b8\u09cd\u09a5\u09be\u09a8 \u09aa\u09b0\u09cd\u09af\u09a8\u09cd\u09a4 \u0985\u0982\u09b6\u0995\u09c7\u09b0 \u09ae\u09be\u09a8 \u09ac\u09c7\u09b0 \u0995\u09b0\u09be \u09b9\u09df\u0964 \u0995\u09cb\u09a8 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u09b2\u0997\u09c7\u09b0 \u0985\u0982\u09b6\u0995 \u09b2\u0997 \u09a4\u09be\u09b2\u09bf\u0995\u09be \u09a5\u09c7\u0995\u09c7 \u09ac\u09c7\u09b0 \u0995\u09b0\u09be \u09af\u09be\u09df\u0964 \u0986\u09ac\u09be\u09b0 \u09a4\u09be \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09c7\u099f\u09b0\u09c7\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7\u0993 \u09ac\u09c7\u09b0 \u0995\u09b0\u09be \u09af\u09be\u09df\u0964<\/span><\/p>\n<h4><b>\u0985\u0982\u09b6\u0995 \u0993 \u09aa\u09c2\u09b0\u09cd\u09a3\u0995\u09c7\u09b0 \u0989\u09a6\u09be\u09b9\u09b0\u09a3:\u00a0<\/b><\/h4>\n<p><span style=\"font-weight: 400;\">0.0000836=<\/span><span style=\"font-weight: 400;\">8.36<\/span><span style=\"font-weight: 400;\">100000<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">=8.36\u00d71<\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\">-5<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u098f\u0996\u09be\u09a8\u09c7 \u09aa\u09c2\u09b0\u09cd\u09a3\u0995 <\/span><span style=\"font-weight: 400;\">-5<\/span><span style=\"font-weight: 400;\"> \u09ac\u09be \u098f\u0995\u09c7 <\/span><span style=\"font-weight: 400;\">5<\/span> <span style=\"font-weight: 400;\">(5<\/span><span style=\"font-weight: 400;\"> \u09ac\u09be\u09b0 \/<\/span><span style=\"font-weight: 400;\">Bar<\/span><span style=\"font-weight: 400;\">)<\/span><span style=\"font-weight: 400;\"> \u09a6\u09cd\u09ac\u09be\u09b0\u09be\u0993 \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09be \u09b9\u09df\u0964\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">log8.36=0.92221<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u098f\u0987 <\/span><span style=\"font-weight: 400;\">0.92221<\/span><span style=\"font-weight: 400;\"> \u0987 \u09b9\u09b2\u09cb \u0985\u0982\u09b6\u0995\u0964<\/span><\/p>\n<h4><b>\u09b8\u09a4\u09b0\u09cd\u0995\u09a4\u09be <\/b><b>(Cautions) <\/b><b>:\u00a0<\/b><\/h4>\n<p><span style=\"font-weight: 400;\">\u0985\u0982\u09b6\u0995 \u09ac\u09be \u09aa\u09c2\u09b0\u09cd\u09a3\u0995\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 <\/span><span style=\"font-weight: 400;\">1\u2264a&lt;10<\/span><span style=\"font-weight: 400;\">\u00a0 \u098f\u0987 \u09a8\u09bf\u09df\u09ae\u099f\u09bf \u09ae\u09c7\u09a8\u09c7 \u099a\u09b2\u09be \u0986\u09ac\u09b6\u09cd\u09af\u0995\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">e<\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\"> \u09ac\u09be\u00a0 <\/span><span style=\"font-weight: 400;\">lnx<\/span><span style=\"font-weight: 400;\"> \u0986\u0995\u09be\u09b0\u09c7 \u09b8\u09cd\u09ac\u09be\u09ad\u09be\u09ac\u09bf\u0995 \u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae \u098f\u09ac\u0982 <\/span><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">10<\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\"> \u0995\u09c7 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae \u09ac\u09b2\u09be \u09b9\u09df\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae\u09c7\u09b0 \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf \u0989\u09b2\u09cd\u09b2\u09c7\u0996 \u09a8\u09be \u09a5\u09be\u0995\u09b2\u09c7 \u09ac\u09c0\u099c\u0997\u09be\u09a3\u09bf\u09a4\u09c0\u09df \u09b0\u09be\u09b6\u09bf\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 <\/span><span style=\"font-weight: 400;\">e<\/span><span style=\"font-weight: 400;\"> \u098f\u09ac\u0982 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 <\/span><span style=\"font-weight: 400;\">10<\/span><span style=\"font-weight: 400;\"> \u0995\u09c7 \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf \u09b9\u09bf\u09b8\u09c7\u09ac\u09c7 \u09a7\u09b0\u09be \u09b9\u09df\u0964<\/span><\/p>\n<h4><b>\u09ae\u09a8\u09c7 \u09b0\u09be\u0996\u09be\u09b0 \u09b8\u09b9\u099c \u0995\u09cc\u09b6\u09b2 <\/b><b>(Easy techniques to remember)<\/b><\/h4>\n<p><span style=\"font-weight: 400;\">\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u09aa\u09c2\u09b0\u09cd\u09a3 \u0985\u0982\u09b6\u09c7 \u09af\u09a4\u0997\u09c1\u09b2\u09cb \u0985\u0982\u0995 \u09a5\u09be\u0995\u09ac\u09c7, \u09b8\u0982\u0996\u09cd\u09af\u09be\u099f\u09bf\u09b0 \u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae\u09c7\u09b0 \u09aa\u09c2\u09b0\u09cd\u09a3\u0995 \u09b9\u09ac\u09c7 \u09b8\u09c7\u0987 \u0985\u0999\u09cd\u0995\u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u099a\u09c7\u09df\u09c7 <\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\"> \u0995\u09ae \u098f\u09ac\u0982 \u09a4\u09be \u09b9\u09ac\u09c7 \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995\u0964\u00a0 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u0989\u09b2\u09cd\u09b2\u09c7\u0996\u09bf\u09a4 \u0985\u0999\u09cd\u0995\u09b8\u0982\u0996\u09cd\u09af\u09be <\/span><span style=\"font-weight: 400;\">m<\/span><span style=\"font-weight: 400;\"> \u09b9\u09b2\u09c7 \u09b8\u0982\u0996\u09cd\u09af\u09be\u099f\u09bf\u09b0 \u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae\u09c7\u09b0 \u09aa\u09c2\u09b0\u09cd\u09a3\u0995 \u09b9\u09ac\u09c7 <\/span><span style=\"font-weight: 400;\">m-1<\/span><span style=\"font-weight: 400;\">\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u09aa\u09c2\u09b0\u09cd\u09a3 \u0985\u0982\u09b6 \u09a8\u09be \u09a5\u09be\u0995\u09b2\u09c7 \u09a6\u09b6\u09ae\u09bf\u0995 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u0993 \u098f\u09b0 \u09aa\u09b0\u09c7\u09b0 \u09aa\u09cd\u09b0\u09a5\u09ae \u09b8\u09be\u09b0\u09cd\u09a5\u0995 \u0985\u0999\u09cd\u0995\u09c7\u09b0 \u09ae\u09be\u099d\u09c7 \u09af\u09a4\u0997\u09c1\u09b2\u09cb <\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\"> \u09a5\u09be\u0995\u09ac\u09c7, \u09b8\u0982\u0996\u09cd\u09af\u09be\u099f\u09bf\u09b0 \u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae\u09c7\u09b0 \u09aa\u09c2\u09b0\u09cd\u09a3\u0995 \u09b9\u09ac\u09c7 <\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\"> \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u099a\u09c7\u09df\u09c7 <\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\"> \u09ac\u09c7\u09b6\u09bf \u098f\u09ac\u0982 \u09a4\u09be \u09b9\u09ac\u09c7 \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u0989\u09b2\u09cd\u09b2\u09bf\u0996\u09bf\u09a4 <\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\"> \u09b8\u0982\u0996\u09cd\u09af\u09be <\/span><span style=\"font-weight: 400;\">k<\/span><span style=\"font-weight: 400;\"> \u09b9\u09b2\u09c7 \u09b8\u0982\u0996\u09cd\u09af\u09be\u099f\u09bf\u09b0 \u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae\u09c7\u09b0 \u09aa\u09c2\u09b0\u09cd\u09a3\u0995 \u09b9\u09ac\u09c7 <\/span><span style=\"font-weight: 400;\">{-(k+1)}<\/span><span style=\"font-weight: 400;\">\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09aa\u09c2\u09b0\u09cd\u09a3\u0995 \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995 \u09b9\u09b2\u09c7 \u09aa\u09c2\u09b0\u09cd\u09a3\u0995\u099f\u09bf\u09b0 \u09ac\u09be\u09ae\u09c7 <\/span><span style=\"font-weight: 400;\">(-)<\/span><span style=\"font-weight: 400;\"> \u099a\u09bf\u09b9\u09cd\u09a8 \u09a8\u09be \u09a6\u09bf\u09df\u09c7 \u0989\u09aa\u09b0\u09c7 \u09ac\u09be\u09b0 (<\/span><span style=\"font-weight: 400;\">k<\/span><span style=\"font-weight: 400;\">) \u09b9\u09bf\u09b8\u09c7\u09ac\u09c7 \u09b2\u09bf\u0996\u09be \u09af\u09be\u09df\u0964\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u09ac\u09c8\u099c\u09cd\u099e\u09be\u09a8\u09bf\u0995 \u09b0\u09c2\u09aa : <\/span><span style=\"font-weight: 400;\">a\u00d71<\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\">n<\/span> <span style=\"font-weight: 400;\">(1\u2264a&lt;10,<\/span> <span style=\"font-weight: 400;\">n\u2208<\/span><span style=\"font-weight: 400;\">Z<\/span><span style=\"font-weight: 400;\">)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09b8\u09cd\u09ac\u09be\u09ad\u09be\u09ac\u09bf\u0995 \u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae <\/span><span style=\"font-weight: 400;\">e<\/span><span style=\"font-weight: 400;\"> \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf\u0995 \u098f\u09ac\u0982 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae <\/span><span style=\"font-weight: 400;\">10<\/span><span style=\"font-weight: 400;\"> \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf\u0995\u0964<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\">0\u2192<\/span> <span style=\"font-weight: 400;\">\u0985\u09b8\u0982\u099c\u09cd\u099e\u09be\u09df\u09bf\u09a4<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\">(-1)\u2192<\/span> <span style=\"font-weight: 400;\">\u0985\u09b8\u0982\u099c\u09cd\u099e\u09be\u09df\u09bf\u09a4<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\">1\u2192<\/span> <span style=\"font-weight: 400;\">\u098f\u09b0 \u09ae\u09be\u09a8 <\/span><span style=\"font-weight: 400;\">0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">log1\u21920<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">e<\/span><span style=\"font-weight: 400;\">e\u21921<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">log<\/span><span style=\"font-weight: 400;\">10<\/span><span style=\"font-weight: 400;\">0.000000001=-9<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">\u0986\u09b2\u09cb\u09b0 \u09ac\u09c7\u0997 <\/span><span style=\"font-weight: 400;\">=3\u00d71<\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\">8<\/span><span style=\"font-weight: 400;\">\u00a0ms<\/span><span style=\"font-weight: 400;\">-1<\/span><span style=\"font-weight: 400;\">\u00a0\u00a0\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">=3\u00d7100000000\u00a0<\/span><span style=\"font-weight: 400;\">ms<\/span><span style=\"font-weight: 400;\">-1<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">=300000000<\/span><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>ax=N\u00a0 a&gt;0.\u00a0a\u22601 \u09b9\u09b2\u09c7, x=logaN \u0995\u09c7 N \u098f\u09b0 a \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf\u0995 \u09b2\u0997 \u09ac\u09b2\u09be \u09b9\u09df\u0964 \u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae\u0995\u09c7 \u09b8\u0982\u0995\u09cd\u09b7\u09c7\u09aa\u09c7 \u09b2\u0997 (log) \u09b2\u09c7\u0996\u09be \u09b9\u09df\u0964 \u09b2\u0997 \u09b2\u09c7\u0996\u09be\u09b0 \u09a8\u09bf\u09df\u09ae- \u09b8\u09c2\u099a\u0995\u09c0\u09df \u098f\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09b9\u09b2\u09cb \u09b2\u0997\u09be\u09b0\u09bf\u09a6\u09ae (Logarithms) \u09b2\u0997\u09c7\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09b9\u09b2\u09cb \u09b8\u09c2\u099a\u0995\u09c0\u09df y=ax \u099c\u09be\u09df\u0997\u09be \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8 \u0995\u09b0\u09b2\u09c7 \u2192x=logay \u00a0logaMNP\u2026=\u00a0logaM+logaN+logaP+\u2026\u00a0 \u0995\u09bf\u09a8\u09cd\u09a4\u09c1, logM\u00b1NlogaM\u00b1logaN MN=M-N<\/p>\n<p> <a class=\"redmore\" href=\"https:\/\/10minuteschool.com\/content\/logarithms-methods-of-logarithm\/\">Read More<\/a><\/p>\n","protected":false},"author":56,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[3036],"tags":[],"_links":{"self":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/9331"}],"collection":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/users\/56"}],"replies":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/comments?post=9331"}],"version-history":[{"count":5,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/9331\/revisions"}],"predecessor-version":[{"id":14470,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/9331\/revisions\/14470"}],"wp:attachment":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/media?parent=9331"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/categories?post=9331"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/tags?post=9331"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}