Evaluate log base 5 of 1/5

Rewrite as an equation.

Rewrite ${\displaystyle {\log }_5\left(\frac{1}{5}\right)=x}$ in exponential form using the definition of a logarithm. If ${\displaystyle x}$ and ${\displaystyle b}$ are positive real numbers and ${\displaystyle b}$ does not equal ${\displaystyle 1}$, then ${\displaystyle {\log }_b\left(x\right)=y}$ is equivalent to ${\displaystyle b^y=x}$.

Create equivalent expressions in the equation that all have equal bases.

Since the bases are the same, the two expressions are only equal if the exponents are also equal.