## Precalculus (6th Edition) Blitzer

$x\approx 2.27$
$3^{x+4}=7^{2x-1}\qquad$ ... 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 $x\approx 2.27$