Answer
True.
Work Step by Step
First, divide both sides of the equation by $a$ to get $$b^t=\frac{n}{a}$$ Next, take the $\log$ of both sides to get $$\log b^t=\log(n/a)$$ Since $\log a^b=b \log a$ for all positive values of $a$, $$t \log b = log(n/a)$$ Finally, divide both sides by $\log b$ to get $$t = \frac{\log(n/a)}{\log b}$$ Thus, the statement is true.