Precalculus (6th Edition) Blitzer

$x\approx 1.14$
$5^{4x+2}=37,500\qquad$ ... apply $\ln$( ) to both sides $\ln 5^{4x+2}=\ln 37,500 \qquad$ ... apply $\log_{b}(M^{p})=p\cdot\log_{b}\mathrm{M}$ $(4x+2)\ln 5=\ln 37,500 \qquad$ ... divide with $\ln 5$ $4x+2=\displaystyle \frac{\ln 37,500}{\ln 5}\qquad$ ... subtract 2 $4x=\displaystyle \frac{\ln 37,500}{\ln 5}-2\qquad$ ... divide with $4$ $x=\displaystyle \frac{\ln 37,500}{4\ln 5}-\frac{1}{2}\qquad$... round to two decimal places $x\approx 1.14$