Answer
$ x\approx 1.14$
Work Step by Step
$ 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$
