Answer
$\log_\frac{3}{4}{\frac{4}{3}}=-1$
Work Step by Step
Given an exponential equation as: $b^x=a$
This equation can be converted into logarithmic form expressed as: $\log_b{a}=x$
Thus, $(\frac{3}{4})^{-1}=\frac{4}{3}$ is equivalent to $\log_\frac{3}{4}{\frac{4}{3}}=-1$