Question

prove that,a^loga^x=x

Answer 1

let x=a^N
now
LHS=a^log a^x=a^log a^(a^N)
from logarithm property
logr^t=tlogr
now use this
=a^log a^(a^N)=a^(Nloga ^a)=a^N
but a^N=x =LHS
hence LHS=RHS