Answer
$x \approx 3.58$
Work Step by Step
Add 7 to both sides of the equation to obtain
$e^{4x-5}-7+7=11,243+7
\\e^{4x-5}=11,250.$
The base in the exponential equation is $e$ so take the natural logarithm on both sides to obtain
$\ln{e^{4x-5}}=\ln{11,250}.$
Use the property $\ln{e^b}=b$ (where b=4x-5) on the left side to obtain
$4x-5 = \ln{11,250}.$
Solve for $x$:
$4x-5+5 = \ln{11,250}+5
\\4x=\ln{11,250} +5
\\x=\dfrac{\ln{11,250}+5}{4}.$
Use a calculator and round-off the answer to two decimal places to obtain
$x \approx 3.58.$
