Answer
$x\approx1.09$
Work Step by Step
Find the natural log of both sides and then pull out the exponent to the left side. Then solve for $x$.
$7^{x+2}=410$
$\ln(7^{x+2})=\ln(410)$
$(x+2)\ln(7)=\ln(410)$
$(x+2)=\frac{\ln(410)}{\ln(7)}$
$x=\frac{\ln(410)}{\ln(7)}-2$
$x\approx1.09$
