Use base change formula $log_ab = \frac{log_xb}{log_xa}$
$log_e2 = \frac{\log_{10}2}{log_{10}e}$ and $log_e100 = \frac{log_{10}100}{log_{10}e}$
Substitute these in the original expression and you get,
$= \frac{\frac{log_{10}2}{log_{10}e}+\frac{log_{10}100}{log_{10}e}}{\frac{log_{10}100}{log_{10}e}}$
Simplify this and you get,
$= \frac{log_{10}2+2}{2}$
You need to know that $log_{10}2 = 0.301$,
Put in above expression and you get,
$= \frac{0.301+2}{2} = 1.1505$
Note: You could have solved this with the virtual calculator during GATE.
