Answer
$ x\approx 2.27$
Work Step by Step
$ 3^{x+4}=7^{2x-1}\qquad $ ... apply $\ln $( ) to both sides
$\ln 3^{x+4}=\ln 7^{2x-1} \qquad $ ... apply $\quad \log_{b}(M^{p})=p\cdot\log_{b}\mathrm{M}$
$(x+4)\ln 3=(2x-1)\ln 7\qquad $ ... distribute
$ x\ln 3+4\ln 3=2x\ln 7-\ln 7\qquad $ ... x to one side...
$ x\ln 3-2x \ln 7 =-4\ln 3-\ln 7\qquad $ ... factor out x
$ x(\ln 3-2\ln 7)=-4\ln 3-\ln 7\qquad $
... divide with $(\ln 3-2\ln 7)$
$ x=\displaystyle \frac{-4\ln 3-\ln 7}{\ln 3-2\ln 7}\qquad $... use calculator and round to two decimal places
$ x\approx 2.27$
