Answer
$t=\dfrac{\log \dfrac{A}{P}}{n \log (a+\dfrac{r}{n})}$
Work Step by Step
The given expression can be written as:
$\dfrac{A}{P}=(a+\dfrac{r}{n})^{tn}$
We need to take log of both sides and apply logarithmic property : $\log a^ b=b \log a$ .
$ \log \dfrac{A}{P}=tn \log (a+\dfrac{r}{n})$
Therefore, our answer is: $t=\dfrac{\log \dfrac{A}{P}}{n \log (a+\dfrac{r}{n})}$
