詳解：換底公式

\(f(x) = {\log _5}x{\rm{ = }}\frac{{\ln x}}{{\ln 5}}\)

\(f'(x) = \frac{{{{\left( {\ln x} \right)}^\prime }}}{{\ln 5}} = \frac{1}{x} \cdot \frac{1}{{\ln 5}}\)