Answer
$x\approx-10.25$
Work Step by Step
Find the natural log of both sides and then pull out the exponent to the left side. Then solve for $x$.
$3^{\frac{x}{7}}=0.2$
$\frac{x}{7}\ln(3)=\ln(0.2)$
$\frac{x}{7}=\frac{\ln(0.2)}{\ln(3)}$
$x=7\times\frac{\ln(0.2)}{\ln(3)}$
$x\approx-10.25$
