Question

# Solve the equation, if possible. (Round your answer to two decimal places, if necessary.)$5^{x}=\frac{1}{125}$

Solution

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$\begin{gathered} {5^x} = \frac{1}{{125}} \\ \textcolor{#4257b2}{{\text{Rewrite }}\frac{1}{{125}}{\text{ as }}\frac{1}{{{5^3}}}} \\ {5^x} = \frac{1}{{{5^3}}} \\ \textcolor{#4257b2}{ {\text{Apply }}\frac{1}{{{a^m}}} = {a^{ - m}}} \\ {5^x} = {5^{ - 3}} \\ \textcolor{#4257b2}{ {\text{Use One - to - One property }}{a^x} = {a^y}{\text{ if and only if }}x = y,{\text{ so}}} \\ x = - 3 \\ \end{gathered}$

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