Question

对数的换底公式怎么用啊

{log(4)3+log(8)3}{log(3)2+log(9)2}这个用对数的换底公式化简．过程写详细点．谢谢啊！

Answer 1

对数的换底公式:一种是化为同底的对数;一种是化为常用对数便于约分等.
{log(4)3+log(8)3}{log(3)2+log(9)2}
=[(lg3/lg4)+(lg3/lg8)][(lg2/lg3)+(lg2/lg9)].......(用了换底公式)
=[(lg3/2lg2)+(lg3/3lg2)][(lg2/lg3)+(lg2/2lg3)]
=[(3lg3+2lg3)/(6lg2)][(2lg2+lg2)/(2lg3)]
=[(5lg3)/(6lg2)][(3lg2)/(2lg3)]...........(通分得到的)
=(5/6)×(3/2)..............................(约分)
=5/4

Answer 2

换底公式怎么用呢？

Answer 3

log(M)N=log(X)N/log(X)M