Answer
$x \approx 1.09$
Work Step by Step
RECALL:
$\ln{a^b} = b \cdot \ln{a}$
Take the natural logarithm of both sides to obtain:
$\ln{7^{x+2}}=\ln{410}$
Use the rule above to obtain:
$(x+2)\ln{7}=\ln{410}$
Divide $\ln{7}$ on both sides to obtain:
$x+2= \dfrac{\ln{410}}{\ln{7}}$
Subtract $2$ on both sides of the equation to obtain:
$x = -2 +\dfrac{\ln{410}}{\ln{7}}$
Use a scientific calculator to obtain:
$x=1.091693192
\\x \approx 1.09$
