高中数学对数怎么写
\u9ad8\u4e2d\u6570\u5b66\u7684\u6240\u6709\u5bf9\u6570\u8ba1\u7b97\u516c\u5f0f \u6025\u554a\u5b9a\u4e49\uff1a
\u3000\u3000\u82e5a^n=b(a>0\u4e14a\u22601)
\u3000\u3000\u5219n=log(a)(b)
\u3000\u3000\u57fa\u672c\u6027\u8d28\uff1a
\u3000\u30001\u3001a^(log(a)(b))=b
\u3000\u30002\u3001log(a)(MN)=log(a)(M)+log(a)(N);
\u3000\u30003\u3001log(a)(M\u00f7N)=log(a)(M)-log(a)(N);
\u3000\u30004\u3001log(a)(M^n)=nlog(a)(M)
\u3000\u3000\u63a8\u5bfc
\u3000\u30001\u3001\u56e0\u4e3an=log(a)(b)\uff0c\u4ee3\u5165\u5219a^n=b\uff0c\u5373a^(log(a)(b))=b\u3002
\u3000\u30002\u3001MN=M\u00d7N
\u3000\u3000\u7531\u57fa\u672c\u6027\u8d281(\u6362\u6389M\u548cN)
\u3000\u3000a^[log(a)(MN)] = a^[log(a)(M)]\u00d7a^[log(a)(N)]
\u3000\u3000\u7531\u6307\u6570\u7684\u6027\u8d28
\u3000\u3000a^[log(a)(MN)] = a^{[log(a)(M)] + [log(a)(N)]}
\u3000\u3000\u53c8\u56e0\u4e3a\u6307\u6570\u51fd\u6570\u662f\u5355\u8c03\u51fd\u6570\uff0c\u6240\u4ee5
\u3000\u3000log(a)(MN) = log(a)(M) + log(a)(N)
\u3000\u30003\u3001\u4e0e\uff082\uff09\u7c7b\u4f3c\u5904\u7406
\u3000\u3000MN=M\u00f7N
\u3000\u3000\u7531\u57fa\u672c\u6027\u8d281(\u6362\u6389M\u548cN)
\u3000\u3000a^[log(a)(M\u00f7N)] = a^[log(a)(M)]\u00f7a^[log(a)(N)]
\u3000\u3000\u7531\u6307\u6570\u7684\u6027\u8d28
\u3000\u3000a^[log(a)(M\u00f7N)] = a^{[log(a)(M)] - [log(a)(N)]}
\u3000\u3000\u53c8\u56e0\u4e3a\u6307\u6570\u51fd\u6570\u662f\u5355\u8c03\u51fd\u6570\uff0c\u6240\u4ee5
\u3000\u3000log(a)(M\u00f7N) = log(a)(M) - log(a)(N)
\u3000\u30004\u3001\u4e0e\uff082\uff09\u7c7b\u4f3c\u5904\u7406
\u3000\u3000M^n=M^n
\u3000\u3000\u7531\u57fa\u672c\u6027\u8d281(\u6362\u6389M)
\u3000\u3000a^[log(a)(M^n)] = {a^[log(a)(M)]}^n
\u3000\u3000\u7531\u6307\u6570\u7684\u6027\u8d28
\u3000\u3000a^[log(a)(M^n)] = a^{[log(a)(M)]*n}
\u3000\u3000\u53c8\u56e0\u4e3a\u6307\u6570\u51fd\u6570\u662f\u5355\u8c03\u51fd\u6570\uff0c\u6240\u4ee5
\u3000\u3000log(a)(M^n)=nlog(a)(M)
\u3000\u3000\u57fa\u672c\u6027\u8d284\u63a8\u5e7f
\u3000\u3000log(a^n)(b^m)=m/n*[log(a)(b)]
\u3000\u3000\u63a8\u5bfc\u5982\u4e0b\uff1a
\u3000\u3000\u7531\u6362\u5e95\u516c\u5f0f\uff08\u6362\u5e95\u516c\u5f0f\u89c1\u4e0b\u9762\uff09[lnx\u662flog(e)(x)\uff0ce\u79f0\u4f5c\u81ea\u7136\u5bf9\u6570\u7684\u5e95]
\u3000\u3000log(a^n)(b^m)=ln(b^m)\u00f7ln(a^n)
\u3000\u3000\u7531\u57fa\u672c\u6027\u8d284\u53ef\u5f97
\u3000\u3000log(a^n)(b^m) = [m\u00d7ln(b)]\u00f7[n\u00d7ln(a)] = (m\u00f7n)\u00d7{[ln(b)]\u00f7[ln(a)]}
\u3000\u3000\u518d\u7531\u6362\u5e95\u516c\u5f0f
\u3000\u3000log(a^n)(b^m)=m\u00f7n\u00d7[log(a)(b)] --------------------------------------------\uff08\u6027\u8d28\u53ca\u63a8\u5bfc \u5b8c\uff09
\u7f16\u8f91\u672c\u6bb5\u51fd\u6570\u56fe\u8c61
\u3000\u30001.\u5bf9\u6570\u51fd\u6570\u7684\u56fe\u8c61\u90fd\u8fc7(1,0)\u70b9.
\u3000\u30002.\u5bf9\u4e8ey=log(a)(n)\u51fd\u6570,
\u3000\u3000\u2460,\u5f530<a<1\u65f6,\u56fe\u8c61\u4e0a\u51fd\u6570\u663e\u793a\u4e3a(0,+\u221e)\u5355\u51cf.\u968f\u7740a \u7684\u589e\u5927,\u56fe\u8c61\u9010\u6e10\u4ee5(1,0)\u70b9\u4e3a\u8f74\u987a\u65f6\u9488\u8f6c\u52a8,\u4f46\u4e0d\u8d85\u8fc7X=1.
\u3000\u3000\u2461\u5f53a>1\u65f6,\u56fe\u8c61\u4e0a\u663e\u793a\u51fd\u6570\u4e3a(0,+\u221e)\u5355\u589e,\u968f\u7740a\u7684\u589e\u5927,\u56fe\u8c61\u9010\u6e10\u4ee5(1.0)\u70b9\u4e3a\u8f74\u9006\u65f6\u9488\u8f6c\u52a8,\u4f46\u4e0d\u8d85\u8fc7X=1.
\u3000\u30003.\u4e0e\u5176\u4ed6\u51fd\u6570\u4e0e\u53cd\u51fd\u6570\u4e4b\u95f4\u56fe\u8c61\u5173\u7cfb\u76f8\u540c,\u5bf9\u6570\u51fd\u6570\u548c\u6307\u6570\u51fd\u6570\u7684\u56fe\u8c61\u5173\u4e8e\u76f4\u7ebfy=x\u5bf9\u79f0.
\u7f16\u8f91\u672c\u6bb5\u5176\u4ed6\u6027\u8d28
\u3000\u3000\u6027\u8d28\u4e00\uff1a\u6362\u5e95\u516c\u5f0f
\u3000\u3000log(a)(N)=log(b)(N)\u00f7log(b)(a)
\u3000\u3000\u63a8\u5bfc\u5982\u4e0b\uff1a
\u3000\u3000N = a^[log(a)(N)]
\u3000\u3000a = b^[log(b)(a)]
\u3000\u3000\u7efc\u5408\u4e24\u5f0f\u53ef\u5f97
\u3000\u3000N = {b^[log(b)(a)]}^[log(a)(N)] = b^{[log(a)(N)]*[log(b)(a)]}
\u3000\u3000\u53c8\u56e0\u4e3aN=b^[log(b)(N)]
\u3000\u3000\u6240\u4ee5 b^[log(b)(N)] = b^{[log(a)(N)]*[log(b)(a)]}
\u3000\u3000\u6240\u4ee5 log(b)(N) = [log(a)(N)]*[log(b)(a)] {\u8fd9\u6b65\u4e0d\u660e\u767d\u6216\u6709\u7591\u95ee\u770b\u4e0a\u9762\u7684}
\u3000\u3000\u6240\u4ee5log(a)(N)=log(b)(N) / log(b)(a)
\u3000\u3000\u516c\u5f0f\u4e8c\uff1alog(a)(b)=1/log(b)(a)
\u3000\u3000\u8bc1\u660e\u5982\u4e0b\uff1a
\u3000\u3000\u7531\u6362\u5e95\u516c\u5f0f log(a)(b)=log(b)(b)/log(b)(a) ----\u53d6\u4ee5b\u4e3a\u5e95\u7684\u5bf9\u6570
\u3000\u3000log(b)(b)=1 =1/log(b)(a) \u8fd8\u53ef\u53d8\u5f62\u5f97: log(a)(b)\u00d7log(b)(a)=1
\u3000\u3000\u5728\u5b9e\u7528\u4e0a\uff0c\u5e38\u91c7\u7528\u4ee510\u4e3a\u5e95\u7684\u5bf9\u6570\uff0c\u5e76\u5c06\u5bf9\u6570\u8bb0\u53f7\u7b80\u5199\u4e3algb,\u79f0\u4e3a\u5e38\u7528\u5bf9\u6570\uff0c\u5b83\u9002\u7528\u4e8e\u6c42\u5341\u8fdb\u4f2f\u5236\u6574\u6570\u6216\u5c0f\u6570\u7684\u5bf9\u6570\u3002\u4f8b\u5982lg10=1,lg100=lg102=2,lg4000=lg\uff08103\u00d74\uff09=3+lg4,\u53ef\u89c1\u53ea\u8981\u5bf9\u67d0\u4e00\u8303\u56f4\u7684\u6570\u7f16\u5236\u51fa\u5bf9\u6570\u8868\uff0c\u4fbf\u53ef\u5229\u7528\u6765\u8ba1\u7b97\u5176\u4ed6\u5341\u8fdb\u5236\u6570\u7684\u5bf9\u6570\u7684\u8fd1\u4f3c\u503c\u3002\u5728\u6570\u5b66\u7406\u8bba\u4e0a\u4e00\u822c\u90fd\u7528\u4ee5\u65e0\u7406\u6570e=2.7182818\u2026\u2026\u4e3a\u5e95\u7684\u5bf9\u6570\uff0c\u5e76\u5c06\u8bb0\u53f7 loge\u3002\u7b80\u5199\u4e3aln\uff0c\u79f0\u4e3a\u81ea\u7136\u5bf9\u6570\uff0c\u56e0\u4e3a\u81ea\u7136\u5bf9\u6570\u51fd\u6570\u7684\u5bfc\u6570\u8868\u8fbe\u5f0f\u7279\u522b\u7b80\u6d01\uff0c\u6240\u4ee5\u663e\u51fa\u4e86\u5b83\u6bd4\u5176\u4ed6\u5bf9\u6570\u5728\u7406\u8bba\u4e0a\u7684\u4f18\u8d8a\u6027\u3002\u5386\u53f2\u4e0a\uff0c\u6570\u5b66\u5de5\u4f5c\u8005\u4eec\u7f16\u5236\u4e86\u591a\u79cd\u4e0d\u540c\u7cbe\u786e\u5ea6\u7684\u5e38\u7528\u5bf9\u6570\u8868\u548c\u81ea\u7136\u5bf9\u6570\u8868\u3002\u4f46\u968f\u7740\u7535\u5b50\u6280\u672f\u7684\u53d1\u5c55\uff0c\u8fd9\u4e9b\u6570\u8868\u5df2\u9010\u6e10\u88ab\u73b0\u4ee3\u7684\u7535\u5b50\u8ba1\u7b97\u5de5\u5177\u6240\u53d6\u4ee3\u3002
\u8c22\u8c22\u63d0\u95ee\u3002\u8fd9\u91cc\u7b80\u8981\u56de\u7b54\u3002
\u5bf9\u6570\u9996\u5148\u662f\u6839\u636e\u5b9e\u9645\u9700\u8981\u521b\u9020\u51fa\u6765\u7684\uff0c\u662f\u822a\u6d77\u3001\u5929\u6587\u5b66\u53d1\u5c55\u7684\u9700\u8981\uff0c\u53ef\u4ee5\u7cbe\u7b80\u8ba1\u7b97\u3002\u5728\u8ba1\u7b97\u673a\u9886\u57df\u5feb\u901f\u5e42\u7b97\u6cd5\u4e5f\u662f\u5bf9\u6570\u7684\u5e94\u7528\u3002\u81ea\u7136\u5bf9\u6570\u4e5f\u6709\u8bb8\u591a\u72ec\u7279\u7684\u6027\u8d28\uff0c\u5728\u7b49\u89d2\u87ba\u7ebf\u7b49\u9ad8\u7b49\u6570\u5b66\u91cc\u90fd\u4f1a\u5e94\u7528\u5230\uff0c\u4f46\u9ad8\u4e2d\u8fd8\u4e0d\u4f1a\u8bb2\u3002
\u5e0c\u671b\u80fd\u89e3\u7b54\u4f60\u7684\u7591\u95ee\u3002
原式=lg20 + (lg25)/2
=lg20 + (1/2)lg25
=lg20 + lg[25^(1/2)]
=lg20 + lg5
=lg(20×5)
=lg100
=2
log以10为底20的对数+1og以100为底25的对数的结果是
=lg20+lg5
=lg100
=2
log以10为底20的对数+1og以100为底25的对数=log以10为底20的对数+1og以10为底5的对数=log以10为底100的对数=2
绛旓細楂樹腑鏁板涓殑lg鍏紡鏄寚浠10涓哄簳鐨瀵规暟鍑芥暟銆傚叾琛ㄧず褰㈠紡涓猴細lg(x)=log10(x)銆備笅闈㈠垪涓句竴浜涘父瑙佺殑lg鍏紡鍙婂叾鎬ц川锛1.lg(1)=0锛氫换浣曟暟鐨勫鏁颁互10涓哄簳鏃讹紝瀵瑰簲鐨勫间负0銆2.lg(10)=1锛10鐨勫鏁颁互10涓哄簳鏃讹紝瀵瑰簲鐨勫间负1銆3.瀵规暟鐨勪箻绉硶鍒欙細lg(a*b)=lg(a)+lg(b)4.瀵规暟鐨勫晢娉曞垯锛歭g(a...
绛旓細1.涓よ竟鍙瀵规暟锛屼互鏍瑰彿2鍑1涓哄簳鏁 x=log(鏍瑰彿2鍑1锛2 2.鍙煡锛歭og2 x+log2 y=log2 (xy)=2 鍒檟y=4锛屽洜涓簒锛寉鈮0 鑰岋紙x+y)鈮2鏍瑰彿锛坸y锛=4 3.1+1/2lg9-lg240=1+lg3-lg锛16*15锛=1+lg3-lg16-lg15 =1+lg3-4lg2-lg3-lg5 =lg10-4lg2-lg5 =lg2+lg5-4lg2-lg5 ...
绛旓細楂樹腑鏁板涓璴og鐭ヨ瘑鐐规湁濡備笅锛1銆佸湪绠鍗曠殑鎯呭喌涓嬶紝涔樻暟涓殑瀵规暟璁℃暟鍥犲瓙銆傛洿涓鑸潵璇达紝涔樺箓鍏佽灏嗕换浣曟瀹炴暟鎻愰珮鍒颁换浣曞疄闄呭姛鐜囷紝鎬绘槸浜х敓姝ｇ殑缁撴灉锛屽洜姝ゅ彲浠ュ浜巄涓嶇瓑浜1鐨勪换浣曚袱涓瀹炴暟b鍜寈璁＄畻瀵规暟銆傚鏋渁鐨剎娆℃柟绛変簬N锛坅>0锛屼笖a鈮1锛夛紝閭ｄ箞鏁皒鍙仛浠涓哄簳N鐨勫鏁帮紙logarithm锛夛紝璁颁綔x=loga N...
绛旓細涓鑸湴锛屽嚱鏁皔=logaX锛坅>0锛屼笖a鈮1锛夊氨鍙仛瀵规暟鍑芥暟锛屽叾涓渓og鈥濇槸鎷変竵鏂噇ogarithm锛堝鏁帮級鐨勭缉鍐欍備腑鏂囧悕 瀵规暟鍑芥暟 澶栨枃鍚 Logarithmic Function 鍒О 瀵瑰嚱鏁 琛ㄨ揪寮 y=logax锛坅>0 & a鈮1锛夋彁鍑鸿 绾︾堪路绾崇毊灏 鏇村 96%鐨勪汉杩樼湅浜 楂樹腑鏁板log鍏紡 楂樹腑鏁板ln鍜宭og ln鍑芥暟鐨勭煡璇嗙偣鍜屽叕寮 ...
绛旓細鍒╃敤鎹㈠簳鍏紡锛歭og100 25 = (1g25)/(lg100) = (lg25)/2 鍘熷紡=lg20 + (lg25)/2 =lg20 + (1/2)lg25 =lg20 + lg[25^(1/2)]=lg20 + lg5 =lg(20脳5)=lg100 =2
绛旓細1銆-log锛坅锛=log1/锛坅锛 杩欐槸瀵规暟杩愮敤閲岀殑鍏紡 2銆乤鐨3/4娆℃柟鏄痑鐨勪笁娆℃柟鍐嶅紑鍥涙鏍瑰彿鐨勬剰鎬濓紝鎵浠ユ剰鎬濆氨鏄痑鐨勪笁娆℃柟=8鐨4娆℃柟锛屽氨鏄痑=8鐨4娆℃柟鍐嶅紑涓夋鏍瑰彿锛屾墍浠=2鐨勫洓娆℃柟灏辨槸16锛宎=16.
绛旓細鐢辨崲搴曞叕寮忥紙鎹㈠簳鍏紡瑙佷笅闈級[lnx鏄痩og(e)(x)锛宔绉颁綔鑷劧瀵规暟鐨勫簳]log(a^n)(b^m)=ln(b^m)梅ln(a^n)鐢卞熀鏈ц川4鍙緱 log(a^n)(b^m)= [m脳ln(b)]梅[n脳ln(a)]= (m梅n)脳{[ln(b)]梅[ln(a)]} 鍐嶇敱鎹㈠簳鍏紡 log(a^n)(b^m)=m梅n脳[log(a)(b)]---锛堟ц川鍙...
绛旓細涓嶅悓鍒嗘瘝鐨勪袱涓垎鏁颁笉鑳界洿鎺ョ浉鍔,瑕佹崲鎴愮浉鍚岀殑鍒嗘瘝鍚庢墠鑳界浉鍔.鍚岀悊搴曚笉鍚岀殑瀵规暟瑕佺浉浜掕繍绠,灏遍渶瑕佹崲鎴愬悓鏍风殑搴.杩欐牱灏变骇鐢熶簡鎹㈠簳鍏紡.鎺ㄥ掍竴锛氳a^b=N鈥︹︹︹憼 鍒檅=logaN鈥︹︹︹憽 鎶娾憽浠ｅ叆鈶犲嵆寰楀鏁版亽绛夊紡锛歛^(logaN)=N鈥︹︹︹憿 鎶娾憿涓よ竟鍙栦互m涓哄簳鐨勫鏁板緱 logaN路logma=logmN 鎵浠 lo...
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