Let and , where and . Prove that for all…

MATHEMATICS · Subjective · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

Let

f(x)=a^{x}

and

g(x)=\log_{a}x

, where

a>0

and

a\neq 1

. Prove that

f\bigl(g(x)\bigr)=x

for all

x>0