Chapter 4 - Section 4.5 - Exponential and Logarithmic Equations - 4.5 Exercises - Page 447: 42

$x=-39$

Changing to exponential form, the given expression, $ \log_5(8-3x)=3 $ is equivalent to \begin{array}{l}\require{cancel} 8-3x=5^3 \\\\ 8-3x=125 \\\\ -3x=125-8 \\\\ -3x=117 \\\\ x=\dfrac{117}{-3} \\\\ x=-39 .\end{array}