Chapter 12 - Exponential Functions and Logarithmic Functions - 12.3 Logarithmic Functions - 12.3 Exercise Set - Page 802: 9

$(b)$

For $x\gt 0$ and $a$ = a positive constant other than 1, $\log_{a}x$ is the exponent to which $a$ must be raised in order to get $x$. Thus, $\log_{5}(5^{x})=m$ means $5^{m}=5^{x}$ so, $m= \log_{5}(5^{x})= x$ case $(b)$