Question

Evaluate the expression ${\log }_5{5}^{-1}$.

Short answer

The simplified value of expression is $-1$.

Step-by-step solution

Step 1. Write down the given expression.

The given expression is ${\log }_5{5}^{-1}$.

Step 2. Simplify the expression.

The given expression ${\log }_5{5}^{-1}$is evaluated as:

$\begin{array}{l}{\log }_5{5}^{-1}={\log }_5\left(\frac{1}{5}\right)\\ ={\log }_5\left(1\right)-{\log }_5\left(5\right)\\ =0-1\\ =-1\end{array}$

Step 3. Conclusion.

The simplified value of expression is $-1$.