Solve the logarithmic equation \( \log _{5}(625)=x \) \( \begin{array}{ll}\text { a.) } x=5 \\ \text { b.) } x=125 \\ \text { c.) } x=4 \\ \text { d.) } x=16\end{array} \)

To solve the logarithmic equation \( \log_{5}(625) = x \), we need to express 625 as a power of 5. Since \( 625 = 5^4 \), we can rewrite the equation as: \[ \log_{5}(5^4) = x \] Using the property of logarithms that states \( \log_{b}(b^a) = a \), we find: \[ x = 4 \] So the answer is \( \text{c.) } x=4 \).