Answer
$10.986=t$
The investment would take 10.986 years.
Work Step by Step
The future value of a continuous compound rate can be described with the following function:
$A(t)=P*e^{rt}$, where $P$ is the amount of investment at $t=0$, $r$ is the compound rate and $t$ is the time since the investment.
In this exercise:
$\frac{A(t)}{P}=3$
$r=0.1$
Also, we can transform our function as:
$A(t)=P*e^{rt}$
$\frac{A(t)}{P}=e^{rt}$
Therefore the question is to calculate $t$, such as:
$3=e^{0.11t}$
$\log_{e}3=\ln3=1.0986=0.1t$
$10.986=t$
The investment would take 10.986 years.