对数中lg的计算方法是什么 要公式 摘抄也行 请注意不是log 满意加悬赏谢谢 求 对数的推导公式的推导过程 答满意再加一百 ！！！

log\u548clg\u6709\u4ec0\u4e48\u533a\u522b\u963f\uff1f\u56de\u7b54\u6ee1\u610f\u7684\u8ffd\u52a0\u5230120\u5206\uff012\u5c0f\u65f6\u5185\u5904\u7406

lg\u662f\u6307\u4ee510\u4e3a\u5e95\u7684\u5bf9\u6570
\u800c\u7528log\u7684\u8bdd\u9700\u8981\u5199\u5e95\u6570\uff0c\u5982log(2)4 = 2 \uff08\u62ec\u53f7\u4e2d\u76842\u662f\u5e95\u6570\uff09

\u4f46\u5728\u5f88\u591a\u8ba1\u7b97\u5668\u4e2d\u7528log\u4ee3\u66fflg\uff0c\u610f\u4e49\u5c31\u662f\u4ee510\u4e3a\u5e95\u7684\u5bf9\u6570
\u5982\u679c\u4f60\u5728\u8ba1\u7b97\u5668\u4e2d\u60f3\u6c42log(2)4\uff0c\u5c31\u9700\u8981\u8f93\u5165 log4 / log2

\u56e0\u4e3alog(2)4 = lg4/lg2 (\u6362\u5e95\u516c\u5f0f) \uff0c\u5728\u8ba1\u7b97\u5668\u4e2d\u5c31\u662f log4/log2\u4e86

\u5bf9\u4e8e\u697c\u4e3b\u7684\u8865\u5145\uff0c\u5176\u5b9e\u662f\u53ef\u4ee5\u8fd9\u6837\u7684\uff0c\u4f46\u4e0d\u662f\u5f88\u6b63\u89c4\uff0c\u5728\u6d4b\u9a8c\u8003\u8bd5\u4e2d\u5c3d\u91cf\u4e0d\u8981\u4f7f\u7528\uff0c\u5c3d\u91cf\u4f7f\u7528lg

\u7528^\u8868\u793a\u4e58\u65b9\uff0c\u7528log(a)(b)\u8868\u793a\u4ee5a\u4e3a\u5e95\uff0cb\u7684\u5bf9\u6570
*\u8868\u793a\u4e58\u53f7\uff0c/\u8868\u793a\u9664\u53f7

\u5b9a\u4e49\u5f0f\uff1a
\u82e5a^n=b(a>0\u4e14a\u22601)
\u5219n=log(a)(b)


\u57fa\u672c\u6027\u8d28\uff1a
1.a^(log(a)(b))=b
2.log(a)(MN)=log(a)(M)+log(a)(N);
3.log(a)(M/N)=log(a)(M)-log(a)(N);
4.log(a)(M^n)=nlog(a)(M)

\u63a8\u5bfc
1.\u8fd9\u4e2a\u5c31\u4e0d\u7528\u63a8\u4e86\u5427\uff0c\u76f4\u63a5\u7531\u5b9a\u4e49\u5f0f\u53ef\u5f97(\u628a\u5b9a\u4e49\u5f0f\u4e2d\u7684[n=log(a)(b)]\u5e26\u5165a^n=b)

2.
MN=M*N
\u7531\u57fa\u672c\u6027\u8d281(\u6362\u6389M\u548cN)
a^[log(a)(MN)] = a^[log(a)(M)] * a^[log(a)(N)]
\u7531\u6307\u6570\u7684\u6027\u8d28
a^[log(a)(MN)] = a^{[log(a)(M)] + [log(a)(N)]}
\u53c8\u56e0\u4e3a\u6307\u6570\u51fd\u6570\u662f\u5355\u8c03\u51fd\u6570\uff0c\u6240\u4ee5
log(a)(MN) = log(a)(M) + log(a)(N)

3.\u4e0e2\u7c7b\u4f3c\u5904\u7406
MN=M/N
\u7531\u57fa\u672c\u6027\u8d281(\u6362\u6389M\u548cN)
a^[log(a)(M/N)] = a^[log(a)(M)] / a^[log(a)(N)]
\u7531\u6307\u6570\u7684\u6027\u8d28
a^[log(a)(M/N)] = a^{[log(a)(M)] - [log(a)(N)]}
\u53c8\u56e0\u4e3a\u6307\u6570\u51fd\u6570\u662f\u5355\u8c03\u51fd\u6570\uff0c\u6240\u4ee5
log(a)(M/N) = log(a)(M) - log(a)(N)

4.\u4e0e2\u7c7b\u4f3c\u5904\u7406
M^n=M^n
\u7531\u57fa\u672c\u6027\u8d281(\u6362\u6389M)
a^[log(a)(M^n)] = {a^[log(a)(M)]}^n
\u7531\u6307\u6570\u7684\u6027\u8d28
a^[log(a)(M^n)] = a^{[log(a)(M)]*n}
\u53c8\u56e0\u4e3a\u6307\u6570\u51fd\u6570\u662f\u5355\u8c03\u51fd\u6570\uff0c\u6240\u4ee5
log(a)(M^n)=nlog(a)(M)




\u5176\u4ed6\u6027\u8d28\uff1a

\u6027\u8d28\u4e00\uff1a\u6362\u5e95\u516c\u5f0f
log(a)(N)=log(b)(N) / log(b)(a)

\u63a8\u5bfc\u5982\u4e0b
N = a^[log(a)(N)]
a = b^[log(b)(a)]

\u7efc\u5408\u4e24\u5f0f\u53ef\u5f97
N = {b^[log(b)(a)]}^[log(a)(N)] = b^{[log(a)(N)]*[log(b)(a)]}

\u53c8\u56e0\u4e3aN=b^[log(b)(N)]
\u6240\u4ee5
b^[log(b)(N)] = b^{[log(a)(N)]*[log(b)(a)]}
\u6240\u4ee5
log(b)(N) = [log(a)(N)]*[log(b)(a)] {\u8fd9\u6b65\u4e0d\u660e\u767d\u6216\u6709\u7591\u95ee\u770b\u4e0a\u9762\u7684}
\u6240\u4ee5log(a)(N)=log(b)(N) / log(b)(a)



\u6027\u8d28\u4e8c\uff1a\uff08\u4e0d\u77e5\u9053\u4ec0\u4e48\u540d\u5b57\uff09
log(a^n)(b^m)=m/n*[log(a)(b)]

\u63a8\u5bfc\u5982\u4e0b
\u7531\u6362\u5e95\u516c\u5f0f[lnx\u662flog(e)(x),e\u79f0\u4f5c\u81ea\u7136\u5bf9\u6570\u7684\u5e95]
log(a^n)(b^m)=ln(a^n) / ln(b^n)
\u7531\u57fa\u672c\u6027\u8d284\u53ef\u5f97
log(a^n)(b^m) = [n*ln(a)] / [m*ln(b)] = (m/n)*{[ln(a)] / [ln(b)]}
\u518d\u7531\u6362\u5e95\u516c\u5f0f
log(a^n)(b^m)=m/n*[log(a)(b)]



\u7d2f\u6b7b\u4e86\u2026\u2026

常用对数　又称“十进对数”.以10为底的对数,用记号“lg”表示.如lgA表示以10为底A的对数,其中A为真数.任一正数的常用对数都可表示成一个整数和一个正的纯小数(或零)的和；整数部分称为对数的“首数”,正的纯小数(或零)称为对数的“尾数”.常用对数有对数表可查.
　　把一个正数用科学记数法表示成一个含有一位整数的小数和10的整数次幂的积的形式然后取常用对数
　　如：lg200=lg(10^2*2)=lg10^2+lg2=2+0.3010
　　lg20=lg(10^1*2)=lg10^1+lg2=1+0.3010
　　lg0,002=lg(10^(-3)*2)=lg10^(-3)+lg2=-3+0.3010

对数Ig是以10为底的对数，如:Ig100=2

扩展阅读：lg常用对数表大全 ... lg等于log多少 ... lg计算公式口诀 ... lg公式大全图解 ... lg计算公式大全 ... log对数计算器 ... 反对数lg-1 ... 对数lg的负一次怎样计算 ... log10和lg10的区别 ...