Question

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

Answer 1

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