数学中的log的具体意思是什么，怎么使用，表示 数学中log什么意思
\u6570\u5b66\u4e2d\u7684log\u7684\u5177\u4f53\u610f\u601d\u662f\u4ec0\u4e48\uff0c\u600e\u4e48\u4f7f\u7528\uff0c\u8868\u793a\uff1f\uff1f\uff1f\uff1f\uff1f\uff1f\uff1f\uff1f\uff1f\uff1f\uff1f\uff1flog\u8868\u793a\u5bf9\u6570\u3002
\u5982\u679ca^n = b\uff08a>0\uff0c\u4e14a\u22601\uff09\uff0c\u90a3\u4e48\u6570n\u53eb\u505a\u4ee5a\u4e3a\u5e95b\u7684\u5bf9\u6570\uff0c\u8bb0\u505an=log(a)b\uff0c\u3010a\u662f\u4e0b\u6807\u3011
\u5176\u4e2d\uff0ca\u53eb\u505a\u201c\u5e95\u6570\u201d\uff0cb\u53eb\u505a\u201c\u771f\u6570\u201d\u3002\u3000\u3000
\u76f8\u5e94\u5730\uff0c\u51fd\u6570y=logaX\u53eb\u505a\u5bf9\u6570\u51fd\u6570\u3002\u5bf9\u6570\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u662f\uff080\uff0c+\u221e\uff09\u3002\u96f6\u548c\u8d1f\u6570\u6ca1\u6709\u5bf9\u6570\u3002
\u5e95\u6570a\u4e3a\u5e38\u6570\uff0c\u5176\u53d6\u503c\u8303\u56f4\u662f\uff080\uff0c1\uff09\u222a\uff081\uff0c+\u221e\uff09\u3002
\u5f53a=10\u65f6\uff0c\u5199\u4f5c\uff1ay=lgx\u3010\u5e38\u7528\u5bf9\u6570\u3011\u3002
\u5f53a=e\u3010\u81ea\u7136\u5bf9\u6570\u7684\u5e95\u6570\u3011\u65f6\uff0c\u5199\u4f5cy=lnx
\u4f8b\uff1a2^3 =8
\u90a3\u4e48 log(2) 8 = 3
log\u8868\u793a\u5bf9\u6570\u3002
\u5982\u679ca^n = b\uff08a>0,\u4e14a\u22601\uff09,\u90a3\u4e48\u6570n\u53eb\u505a\u4ee5a\u4e3a\u5e95b\u7684\u5bf9\u6570,\u8bb0\u505an=log(a)b,\u3010a\u662f\u4e0b\u6807\u3011\u5176\u4e2d,a\u53eb\u505a\u201c\u5e95\u6570\u201d,b\u53eb\u505a\u201c\u771f\u6570\u201d\u3002
\u4e00\u822c\u5730\uff0c\u51fd\u6570y=logax\uff08a>0\uff0c\u4e14a\u22601\uff09\u53eb\u505a\u5bf9\u6570\u51fd\u6570\uff0c\u4e5f\u5c31\u662f\u8bf4\u4ee5\u5e42\uff08\u771f\u6570\uff09\u4e3a\u81ea\u53d8\u91cf\uff0c\u6307\u6570\u4e3a\u56e0\u53d8\u91cf\uff0c\u5e95\u6570\u4e3a\u5e38\u91cf\u7684\u51fd\u6570\uff0c\u53eb\u5bf9\u6570\u51fd\u6570\u3002
\u5176\u4e2dx\u662f\u81ea\u53d8\u91cf\uff0c\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u662f\uff080\uff0c+\u221e\uff09\uff0c\u5373x>0\u3002\u5b83\u5b9e\u9645\u4e0a\u5c31\u662f\u6307\u6570\u51fd\u6570\u7684\u53cd\u51fd\u6570\uff0c\u53ef\u8868\u793a\u4e3ax=ay\u3002\u56e0\u6b64\u6307\u6570\u51fd\u6570\u91cc\u5bf9\u4e8ea\u7684\u89c4\u5b9a\uff0c\u540c\u6837\u9002\u7528\u4e8e\u5bf9\u6570\u51fd\u6570\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u7279\u6b8a\u7684\u5bf9\u6570\uff1a
\uff081\uff09ln\u3002\u81ea\u7136\u5bf9\u6570\u4ee5\u5e38\u6570e\u4e3a\u5e95\u6570\u7684\u5bf9\u6570\u3002\u8bb0\u4f5clnN(N>0)\u3002\u5728\u7269\u7406\u5b66\uff0c\u751f\u7269\u5b66\u7b49\u81ea\u7136\u79d1\u5b66\u4e2d\u6709\u91cd\u8981\u7684\u610f\u4e49\u3002\u4e00\u822c\u8868\u793a\u65b9\u6cd5\u4e3alnx\u3002\u6570\u5b66\u4e2d\u4e5f\u5e38\u89c1\u4ee5logx\u8868\u793a\u81ea\u7136\u5bf9\u6570\u3002
\uff082\uff09LG\uff08\u4ee510\u4e3a\u5e95\u7684\u5bf9\u6570\uff09\u5bf9\u6570\u51fd\u6570lg\uff0c\u662f\u4ee510\u4e3a\u5e95\u7684\u5bf9\u6570\uff08\u5e38\u7528\u5bf9\u6570\uff09\uff0c\u5982lg 10=1\u3002lg\u5373\u4e3alog10\u3002
\u53c2\u8003\u8d44\u6599\uff1a\u767e\u5ea6\u767e\u79d1\u2014\u2014\u5bf9\u6570
y=loga x,a>0且a/=1,是有理数
和y=a^x是互为反函数，y=loga x是y=a^x的反函数的同时，y=a^x也是y=loga x的反函数，
横过（1，0）点。
比如log2 4=log2 2^2=2log2 2=2x1=2.
绛旓細log鍦ㄩ珮涓鏁板閲琛ㄧず瀵规暟銆備竴鑸湴锛屽嚱鏁皔=logax锛坅>0锛屼笖a鈮1锛夊彨鍋氬鏁板嚱鏁帮紝涔熷氨鏄浠ュ箓锛堢湡鏁帮級涓鸿嚜鍙橀噺锛屾寚鏁颁负鍥犲彉閲忥紝搴曟暟涓哄父閲忕殑鍑芥暟锛屽彨瀵规暟鍑芥暟銆傞氬父鎴戜滑灏嗕互10涓哄簳鐨勫鏁板彨甯哥敤瀵规暟锛坈ommon logarithm锛夛紝骞舵妸log10N璁颁负lgN銆傚彟澶栵紝鍦ㄧ瀛﹁鏁颁腑甯镐娇鐢ㄤ互鏃犵悊鏁癳=2.71828路路路涓哄簳鏁...
绛旓細Log鏄瀵规暟锛坙ogarithm锛夌殑绠绉帮紝灞炰簬楂樼瓑鏁板涓殑鍐呭銆傜畝鍗曟潵璇达紝瀵规暟灏辨槸鏌愪竴涓暟鍦ㄨ瀹氱殑鐗瑰畾搴曟暟涓嬫墍寰楃殑骞傛銆傛瘮濡log2 8锛屽叾鎰忔涓衡滀互2涓哄簳锛屼娇寰2鐨勫嚑娆℃柟绛変簬8鈥濓紝缁撴灉涓3銆傚洜姝わ紝瀵规暟涔熻瑙嗕负鏄竴绉嶆暟鍊肩殑杞崲鏂瑰紡锛屽彲浠ュ皢澶嶆潅鐨勪箻闄ゆ硶杞崲涓虹畝鍗曠殑鍔犲噺杩愮畻銆侺og鍦ㄦ暟瀛︿笂鐨勫簲鐢ㄩ潪甯稿箍娉涳紝...
绛旓細鏁板涓殑log鏄瀵规暟鐨勬剰鎬銆傚鏁版槸涓绉嶆暟瀛﹁繍绠楋紝鐢ㄦ潵琛ㄧず涓涓暟鍦ㄦ煇涓熀鏁颁笅鐨勬寚鏁般備緥濡傦紝浠10涓哄熀鏁扮殑瀵规暟锛岃〃绀轰竴涓暟鏄10鐨勫灏戞鏂广傚鏋滀竴涓暟x鍦ㄤ互10涓哄熀鏁扮殑瀵规暟涓嬬殑鍊兼槸y锛岄偅涔堝彲浠ヨ〃绀轰负log10(x)=y銆傚鏁板湪鏁板鍜岀瀛﹂鍩熸湁鐫骞挎硾鐨勫簲鐢紝渚嬪鍦ㄨ绠楁満绉戝銆佺墿鐞嗗銆佸寲瀛︾瓑棰嗗煙涓兘鏈夌潃...
绛旓細log鍦ㄩ珮涓鏁板閲琛ㄧず瀵规暟銆備竴鑸湴锛屽嚱鏁皔=logax锛坅>0锛屼笖a鈮1锛夊彨鍋氬鏁板嚱鏁帮紝涔熷氨鏄浠ュ箓锛堢湡鏁帮級涓鸿嚜鍙橀噺锛屾寚鏁颁负鍥犲彉閲忥紝搴曟暟涓哄父閲忕殑鍑芥暟锛屽彨瀵规暟鍑芥暟銆傞氬父鎴戜滑灏嗕互10涓哄簳鐨勫鏁板彨甯哥敤瀵规暟锛坈ommon logarithm锛夛紝骞舵妸log10N璁颁负lgN銆傚彟澶栵紝鍦ㄧ瀛﹁鏁颁腑甯镐娇鐢ㄤ互鏃犵悊鏁癳=2.71828路路路涓哄簳鏁...
绛旓細log琛ㄧず瀵规暟銆傚鏋渁^n = b锛坅>0锛屼笖a鈮1锛夛紝閭ｄ箞鏁皀鍙仛浠涓哄簳b鐨勫鏁帮紝璁板仛n=log(a)b锛屻恆鏄笅鏍囥戝叾涓紝a鍙仛鈥滃簳鏁扳濓紝b鍙仛鈥滅湡鏁扳濄傜浉搴斿湴锛屽嚱鏁皔=logaX鍙仛瀵规暟鍑芥暟銆傚鏁板嚱鏁扮殑瀹氫箟鍩熸槸锛0锛+鈭烇級銆傞浂鍜岃礋鏁版病鏈夊鏁般傚簳鏁癮涓哄父鏁帮紝鍏跺彇鍊艰寖鍥存槸锛0锛1锛夆埅锛1锛+鈭烇級銆傚綋a...
绛旓細log鏄涓涓鏁板鍑芥暟锛屸渓ogarithm鈥濈殑缂╁啓锛屽畠鏄寚涓涓暟浠ユ煇涓缁欏畾鐨勫簳鏁颁负搴曟暟鐨勫鏁般傛崲鍙ヨ瘽璇达紝濡傛灉鎴戜滑鐭ラ亾涓涓熀鏁帮紙搴曟暟锛夊拰瀹冪殑瀵规暟锛岄偅涔堟垜浠彲浠ラ氳繃姹傚簳鏁扮殑瀵规暟鏉ヨ绠楄繖涓暟銆備緥濡傦紝濡傛灉a鏄竴涓鏁帮紝b鏄竴涓ぇ浜0涓斾笉绛変簬1鐨勬鏁帮紝鍒檒ogb(a)绛変簬浠涓哄簳a鐨勫鏁般俵og鍦ㄦ棩甯哥敓娲讳腑鏈夎澶...
绛旓細鍦ㄩ珮涓鏁板涓锛"log"浠ｈ〃瀵规暟銆傚鏁板嚱鏁扮殑涓鑸舰寮忔槸y=log_a(x)锛屽叾涓璦鏄竴涓ぇ浜0涓斾笉绛変簬1鐨勫父鏁般傝繖涓嚱鏁板皢涓涓暟鐨勫箓锛堝嵆鐪熸暟锛変綔涓鸿嚜鍙橀噺锛屾寚鏁颁綔涓哄洜鍙橀噺锛屽簳鏁板垯鏄浐瀹氱殑銆傚綋鎴戜滑浠10涓哄簳鏃讹紝杩欑瀵规暟琚О涓哄父鐢ㄥ鏁帮紝閫氬父璁颁负lg(N)銆傚湪绉戝璁℃暟娉曚腑锛岀粡甯镐娇鐢ㄤ互e锛堢害绛変簬2.71828锛変负...
绛旓細log鍦ㄩ珮涓鏁板閲琛ㄧず瀵规暟銆傚鏋渁^n = b锛坅>0,涓攁鈮1锛,閭ｄ箞鏁皀鍙仛浠涓哄簳b鐨勫鏁,璁板仛n=log(a)b,銆恆鏄笅鏍囥戝叾涓,a鍙仛鈥滃簳鏁扳,b鍙仛鈥滅湡鏁扳濄備竴鑸湴锛屽嚱鏁皔=logax锛坅>0锛屼笖a鈮1锛夊彨鍋氬鏁板嚱鏁帮紝涔熷氨鏄浠ュ箓锛堢湡鏁帮級涓鸿嚜鍙橀噺锛屾寚鏁颁负鍥犲彉閲忥紝搴曟暟涓哄父閲忕殑鍑芥暟锛屽彨瀵规暟鍑芥暟銆傚叾涓...
绛旓細log鏄瀵规暟鍑芥暟鐨勬剰鎬銆
绛旓細瑙ｏ細log鏄瀵规暟鍑芥暟锛寉=loga x,a>0涓攁/=1,鏄湁鐞嗘暟 鍜寉=a^x鏄簰涓哄弽鍑芥暟锛寉=loga x鏄痽=a^x鐨勫弽鍑芥暟鐨勫悓鏃讹紝y=a^x涔熸槸y=loga x鐨勫弽鍑芥暟锛屾í杩囷紙1锛0锛夌偣銆傛瘮濡俵og2 4=log2 2^2=2log2 2=2x1=2.
