Answer
See explanations.
Work Step by Step
To double means $A=2P$, from $A=P(1+\frac{r}{n})^{tn}$, solve for $t$:
$2P=P(1+\frac{r}{n})^{tn}\longrightarrow (1+\frac{r}{n})^{tn}=2 \longrightarrow t(n)log_2(1+\frac{r}{n})=log_22 \longrightarrow t\ log_2(1+\frac{r}{n})^n=1$,
thus $t=\frac{1}{log_2(1+\frac{r}{n})^n}$
