Answer
$x \approx 1.12$
Work Step by Step
Divide both sides of the equation by 4 to obtain
$e^{7x}=\dfrac{10,273}{4}.$
The base in the exponential equation is $e$, so take the natural logarithm on both sides to obtain
$\ln{e^{7x}}=\ln{\frac{10273}{4}}.$
Use the property $\ln{e^b}=b$ (where b=7x) on the left side to obtain
$7x = \ln{\frac{10273}{4}}.$
Divide both sides by $7$ to obtain
$x=\dfrac{\ln{\frac{10273}{4}}}{7}.$
Use a calculator and round-off the answer to two decimal places to obtain
$x \approx 1.12.$
