Answer
$x \approx 0.188$
Work Step by Step
First, divide both sides by $4$ to get $$13^{3x}=\frac{17}{4}$$ Take the natural log of both sides to get $$\ln 13^{3x} = \ln (17/4)$$ Since $\ln a^b=b \ln a$, the equation becomes $$3x \ln 13 = \ln (17/4)$$ Divide both sides by $3\ln 13$ to get $$x=\frac{\ln (17/4)}{3 \ln 13}\approx0.188$$
