Answer
$ x\approx 1.43$
Work Step by Step
$ e^{12-5x}-7=123\qquad $ ... add 7 to both sides
$ e^{12-5x}=130\qquad $ ... apply $\ln $( ) to both sides
$\ln e^{12-5x}=\ln 130\qquad $ ... apply basic property, $\log_{b}b^{x}=x $
$12-5x= \ln 130\qquad $ ... add $5x-\ln 130$ to both sides
$ 12-\ln 130=5x\qquad $...divide both sides with $5$
$ x=\displaystyle \frac{12-\ln 130}{5}\qquad $... round to two decimal places
$ x\approx 1.43$