# Solve for x: 5^(3x + 24) = 1

Solve for x:
${5}^{3x+24}=1$
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Consider the equation ${5}^{3x+24}=1$
Taking natural logarithms bot sides:
$\mathrm{ln}{5}^{3x+24}=\mathrm{ln}1\phantom{\rule{0ex}{0ex}}\mathrm{ln}{5}^{3x+24}=0\phantom{\rule{0ex}{0ex}}\left(3x+24\right)\mathrm{ln}5=0\phantom{\rule{0ex}{0ex}}3x+24=0\phantom{\rule{0ex}{0ex}}3x=-24\phantom{\rule{0ex}{0ex}}x=\frac{-24}{3}\phantom{\rule{0ex}{0ex}}x=-8$
Therefore, the solution is x=-8