Answer
$\approx 6.9\%$
Work Step by Step
Re-arrange as: $2=e^{10 r}$
We need to take $\ln $ of each side of the equation.
$\ln 2 =\ln e^{10 r}$
Use the logarithmic property $\ln e^a =a $ with $ a=10r $ to obtain
$\ln 2= 10r \implies r = \dfrac{\ln 2}{10} \approx 0.069$ or, $\approx 6.9\%$
We can see that the money will be doubled in 10 years with an interest rate of $\approx 6.9\%$ .
