高中数学，对数的运算 高中数学对数型运算
\u9ad8\u4e2d\u6570\u5b66\u5bf9\u6570\u8fd0\u7b97\u6240\u6709\u516c\u5f0f\u3002\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
\u5f85\u7eed\uff0c\u6211\u6b63\u5728\u52aa\u529b\u7eed\u5199
详细步骤写在纸上了，行家正解
答案是1
第一个括号里面是log62的平方，然后提取公因式，然后log6 36是2
然后就变成了2*log62，所以答案是一
主要考点是对数的加减
分析：1-log(6)3=log(6)6-log(6)3=log(6)(6/3)=log(6)2
log(6)4=log(6)（2^2）=2log(6)2
原式=【【log(6)2】^2+log(6)2Xlog(6)18】/log(6)4
=【log(6)2X【log(6)2+log(6)18】】/log(6)4
=【log(6)2X【log(6)2X18】】/log(6)4
=【log(6)2Xlog(6)36】/log(6)4
=2log(6)2/2log(6)2
=1
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绛旓細璇︾粏姝ラ鍐欏湪绾镐笂浜嗭紝琛屽姝ｈВ
