Answer
$x \approx 1.09$
Work Step by Step
The base in the exponential equation is $7$, so take the natural logarithm on both sides to obtain
$\ln{7^{x+2}}=\ln{410}.$
Use the power rule $\ln{a^x}=x\ln{a}$ to bring down the exponent:
$(x+2)\ln{7} = \ln{410}.$
Divide by $\ln{7}$ to obtain
$x+2 = \dfrac{\ln{410}}{\ln{7}}.$
Subtract $2$ from both sides to obtain
$x = \dfrac{\ln{410}}{\ln{7}}-2.$
Use a calculator and round-off the answer to two decimal places to obtain
$x \approx 1.09.$
