1.4.1 * Let $a$ be a positive real number not equal to 1. The function $f(x)$ satisfies: $f\left(a^{x}\right)=x$. Find the values of $f(1)$ and $f(2)$.
By setting $x=0$ and $x=\log _{a} 2$ in the conditional expression, we get $f(1)=0, f(2)=\log _{a} 2$.