Chapter 12 - Exponential Functions and Logarithmic Functions - 12.6 Solving Exponential Equations and Logarithmic Equations - 12.6 Exercise Set - Page 825: 46

$x=-59$

In exponential form, the given logarithmic equation, $ \log_5(7-2x)=3 ,$ is equivalent to \begin{array}{l}\require{cancel} 7-2x=5^3 .\end{array} Hence, the value of the variable that satisfies the given equation is \begin{array}{l}\require{cancel} 7-2x=125 \\\\ -2x=125-7 \\\\ -2x=118 \\\\ x=\dfrac{118}{-2} \\\\ x=-59 .\end{array}