Answer
$t\approx6.960$
Work Step by Step
Take $\ln$ of both sides of the equation:
$$\ln \left(1+\frac{0.10}{12}\right)^{12t}=\ln 2$$ $$12t\ln\left(1+\frac{0.10}{12}\right)=\ln 2$$ $$t=\frac{\ln 2}{12\ln\left(1+\frac{0.10}{12}\right)}$$ $$t\approx6.960$$
