若a>0,a的2/3次方=4/9,则log2/3 a=

Question

若a>0,a的2/3次方=4/9,则log2/3 a=

Answer 1

答案是 -3
首先在a的2/3次方=4/9两边取2/3的对数,有
log2/3(a的2/3次方)=log2/3(4/9)=-2
log2/3 a=2/3*log2/3(a的2/3次方)=2/3*(-2)=-3