Answer
$x \approx 1.12$
Work Step by Step
Divide $4$ on both sides of the equation to obtain:
$e^{7x}=\dfrac{10,273}{4}$
RECALL:
$\ln{e^m}=m$
Take the natural logarithm of both sides to obtain:
$\ln{e^{7x}}=\ln{(\frac{10,273}{4})}$
Use the rule above to obtain:
$7x=\ln{(\frac{10,273}{4})}$
Divide both sides by $7$ to obtain:
$x = \dfrac{\ln{(\frac{10,273}{4})}}{7}$
Use a scientific calculator to obtain:
$x=1.121568573
\\x \approx 1.12$
