$I = {I_0}{(10)^{\frac{L}{{10}}}} = {I_0}{e^{\left( {\ln 10} \right)\frac{L}{{10}}}}$

$\frac{\mathrm{dI}}{\mathrm{dL}}=\frac{\ln 10}{10} \mathrm{I}$

${\frac{\mathrm{dI}}{\mathrm{I}}=\frac{\ln 10}{10} \mathrm{dL}} $

${\int_{\mathrm{I}}^{2 \mathrm{I}} \frac{\mathrm{d} \mathrm{I}}{\mathrm{I}}=\frac{\ln 10}{10} \int_{0}^{\mathrm{t}} \frac{\mathrm{dL}}{\mathrm{dt}} \mathrm{dt}} $

${\ln 2=\frac{\ln 10}{10} \int_{0}^{\mathrm{t}}(1) \mathrm{d} \mathrm{t}} $

${\rm{t}} \simeq 3\,{\rm{years}}$