Answer
$x \approx -10.25$
Work Step by Step
The base in the exponential equation is $3$, so take the natural logarithm on both sides to obtain
$\ln{(3^{\frac{x}{7}})}=\ln{0.2}.$
Use the power rule $\ln{a^x}=x\ln{a}$ to bring down the exponent:
$(\frac{x}{7})\ln{3} = \ln{0.2}.$
Divide both sides by $\ln{3}$ to obtain
$\dfrac{x}{7} = \dfrac{\ln{0.2}}{\ln{3}}.$
Multiply both sides by $7$ to obtain
$x = 7 \cdot \dfrac{\ln{0.2}}{\ln{3}}.$
Use a calculator and round-off the answer to two decimal places to obtain
$x \approx -10.25.$
