Answer
In both cases, the formula for change-of-base is used.
$\displaystyle \log_{b}M=\frac{\log_{a}M}{\log_{a}b}$
In the first case, we changed $\log_{2}$ to $\log$ (base 10).
$\displaystyle \log_{2}5=\frac{\log 5}{\log 2}$
In the second case, we changed $\log_{2}$ to $\ln$ (base $e$).
$\displaystyle \log_{2}5=\frac{\ln 5}{\ln 2}$
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