若a>0,a^(2/3)=4/9,则log(1/4)a=?

来源：百度知道 编辑：UC知道 时间：2024/05/18 16:46:24
化简后的答案?

a>0,a^(2/3)=4/9,
log(1/4) a^(2/3)=log(1/4) 4/9
2/3*log(1/4)a=log(1/4)(2/3)^2
log(1/4)a=3/2*2log(1/4) (2/3)
=3log(1/4) (2/3)
=3(log(1/4)2 -log(1/4)3)
=-3/2(log2 2-log2 3)
=3/2*log2(3)-3/2

a^(2/3)=4/9
a^2=4^3/9^3
a>0
a=8/27
log(1/4)a=log(1/4)8/27
=-3/2*log(2)2/3

两边平方
a^3=16/81
log(1/4)a=4log(1/4)(2/3)=-2log2(2/3)=-2(1-log(2)3)