Answer
$x\approx3.58$
Work Step by Step
Find the natural log of both sides and then pull out the exponent to the left side ($\ln$ and $e$ cancel each other out). Then solve for $x$.
$e^{4x-5}-7=11243$
$e^{4x-5}=11250$
$4x-5=\ln(11250)$
$4x=\ln(11250)+5$
$x=\frac{\ln(11250)+5}{4}$
$x\approx3.58$
