设ab是正数,且a的b次方=b的a次方,b=9a,则a的值[]A1/9B9的-1/9次方C9的-1/3次方D3的-1/4次方Tellmewhy

Question

设a b是正数,且a的b次方=b的a次方,b=9a,则a的值[ ] A 1/9 B 9的-1/9次方 C 9的-1/3次方 D 3的-1/4次方
Tell me why

Answer 1

a^b=b^a代入b=9a=>a^(9a)=9^a*a^a =>a^(8a)=(a^8)^a=9^a =>a^8=9 =>a=3^(1/4)