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To write the given equation in exponential form, we will recall the definition of a logarithm. $\begin{gathered} \log_{{\color{#0000FF}{b}}}({\color{#FF0000}{x}})=\textcolor{darkviolet}{y} \quad \Leftrightarrow \quad {\color{#FF0000}{x}}={\color{#0000FF}{b}}^{\textcolor{darkviolet}{y}} \end{gathered}$ This means that $y$ is the exponent to which $b$ must be raised to get $x.$ In our exercise, $4$ is the exponent to which $5$ must be raised to get $625.$ $\begin{gathered} \log_{{\color{#0000FF}{5}}}({\color{#FF0000}{625}})=\textcolor{darkviolet}{4} \quad \Leftrightarrow \quad {\color{#FF0000}{625}}={\color{#0000FF}{5}}^{\textcolor{darkviolet}{4}} \end{gathered}$