(log2^5+log4^125)(log3^2)/(log(根号3)^5 要具体的过程,

(1) lg5+lg20+(lg2)² =lg100+(lg2)²=2+(lg2)²
(2)log2^5的底数是多少?

（log2 5+log4 0.2)*(log5 2+log25 0.5)
=(log4 25 +log4 0.2)*(log25 4 +log25 0.5)
=(log4 5)*(log25 2)
=0.5*(log2 5)*0.5*(log5 2)
=0.25

先介绍对数函数的换底公式：log(a)b=lgb/lga
证明：设log(a)b=t
则a^t=b,两边取以10为底的对数
lga^t=lgb
tlga=lgb
所以t=lgb/lga
所以log(a)b=lgb/lga
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log2^5 (3)=lg3/lg2^5=lg3/(5lg2)=(1/5)(lg3/lg2)=(1/5)log2 (3)
即log2^5 (3)=(1/5)log2 (3)

先介绍换底公式：log(a)b=lgb/lga
证明：设log(a)b=t
则a^t=b,两边取以10为底的对数
lga^t=lgb
tlga=lgb
所以t=lgb/lga
所以log(a)b=lgb/lga
＝＝＝＝＝＝＝＝＝＝＝
log(8)9=a ==> lg9/lg8=a ==> 2lg3/(3lg2)=a ==> lg3=(3a/2)lg2
log(2)5=b ==> lg5/lg2=b ==> (lg10-lg2)/lg2=b ==> lg2=1/(b+1)
由此可得,lg3=3a/[2(b+1)]

log2^5*log3^2倍根号2*log5^9=lg5*lg2倍根号2*lg9/(lg2*lg3*lg5)
=3*lg5*lg2*lg3/(lg2*lg3*lg5)=3

对数换底公式
loga(b) = logc(b)/logc(a), 其中a,b,c为底.
上式
2^3+log2^5不知道对数的低是多少,而且其没法直接计算出数值,只能进行简单的变形8+5log2,要计算数值只能用计算器或是查对数表了