换底公式求解换底公式loga^b=logc^b/logc^a 这个公式是怎么推导出来的啊?中间为什么会出来一个c啊?还有

令logc^b=x,logc^a=y,则
b=c^x,a=c^y,loga^b=x/y
b=a^(x/y)=(c^y)^(x/y)=c^x
loga^b=log(a,a^(x/y))=x/y=logc^b/logc^a
c就是换后的底!
1.loga^c*logc^a=1
=lgc/lga*lga/lgc=1
2.log2^3*log3^4*log4^5*log5^2=1
=lg3/lg2*lg4/lg3*lg5/lg4*lg2/lg5=1
3.(log4^3+log8^3)*(log3^2+log9^2)
=(lg3/lg4+lg3/lg8)*(lg2/lg3+lg2/lg9)
=(lg3/2lg2+lg3/3lg2)*(lg2/lg3+lg2/2lg3)
=5/6*lg3/lg2*3/2*lg2/lg3
=5/6*3/2
=5/4

1.loga^c*logc^a=(logk^c/logk^a)*(logk^a/logk^c)=1
2.log2^3*log3^4*log4^5*log5^2=（lg3/lg2）*（lg4/lg3）*（lg5/lg4）*（lg2/lg5）=1
3.
.(log4^3+log8^3)*(log3^2+log9^2)=(1/2log2^3+1/3log2^3)*(log3^2+1/2log3^2)=5/6log2^3*3/2log3^2=5/4

题有人回答 了，我就给你提供个推导公式吧

.loga^c*logc^a=1
2.log2^3*log3^4*log4^5*log5^2=1
3.(log4^3+log8^3)*(log3^2+log9^2)=15