e与ln的转化公式考研 e与ln的转化公式？
\u6c42\u95eeln\u548ce\u5982\u4f55\u4e92\u76f8\u8f6c\u6362\u5982\u56fe\u6240\u793a\uff1a
\u7b80\u5355\u7684\u8bf4\u5c31\u662fln\u662f\u4ee5e\u4e3a\u5e95\u7684\u5bf9\u6570\u51fd\u6570b=e^a\u7b49\u4ef7\u4e8ea=lnb\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\u82e5\u4e3a\u4e86\u907f\u514d\u4e0e\u57fa\u4e3a10\u7684\u5e38\u7528\u5bf9\u6570lgx\u6df7\u6dc6\uff0c\u53ef\u7528\u201c\u5168\u5199\u201d\u33d2ex\u3002
\u5e38\u6570e\u7684\u542b\u4e49\u662f\u5355\u4f4d\u65f6\u95f4\u5185\uff0c\u6301\u7eed\u7684\u7ffb\u500d\u589e\u957f\u6240\u80fd\u8fbe\u5230\u7684\u6781\u9650\u503c\u3002
\u6269\u5c55\u8d44\u6599
\u5bf9\u6570\u7684\u8fd0\u7b97\u6cd5\u5219\uff1a
1\u3001log(a) (M\u00b7N\uff09=log(a) M+log(a) N
2\u3001log(a) (M\u00f7N)=log(a) M-log(a) N
3\u3001log(a) M^n=nlog(a) M
4\u3001log(a)b*log(b)a=1
5\u3001log(a) b=log (c) b\u00f7log (c) a
\u6307\u6570\u7684\u8fd0\u7b97\u6cd5\u5219\uff1a
1\u3001[a^m]\u00d7[a^n]=a^(m\uff0bn) \u3010\u540c\u5e95\u6570\u5e42\u76f8\u4e58\uff0c\u5e95\u6570\u4e0d\u53d8\uff0c\u6307\u6570\u76f8\u52a0\u3011
2\u3001[a^m]\u00f7[a^n]=a^(m\uff0dn) \u3010\u540c\u5e95\u6570\u5e42\u76f8\u9664\uff0c\u5e95\u6570\u4e0d\u53d8\uff0c\u6307\u6570\u76f8\u51cf\u3011
3\u3001[a^m]^n=a^(mn) \u3010\u5e42\u7684\u4e58\u65b9\uff0c\u5e95\u6570\u4e0d\u53d8\uff0c\u6307\u6570\u76f8\u4e58\u3011
4\u3001[ab]^m=(a^m)\u00d7(a^m) \u3010\u79ef\u7684\u4e58\u65b9\uff0c\u7b49\u4e8e\u5404\u4e2a\u56e0\u5f0f\u5206\u522b\u4e58\u65b9\uff0c\u518d\u628a\u6240\u5f97\u7684\u5e42\u76f8\u4e58\u3011
就是ln是以e为底的对数函数b=e^a等价于a=lnb。自然对数以常数e为底数的对数。
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