Answer
(a). $B=74.914$
(b). $I=10^{-2.5}$
(c).The ratio is $10^{2.5}:3.1$
Work Step by Step
From the definition of decibel level we see that,
$B=10\log \frac{I}{I_0}$,
(a). $I_0=10^{-12}$, and $I=3.1\times10^{-5}$,
$B=10\log \frac{3.1\times10^{-5}}{10^{-12}}$,
$B=10(\log 3.1\times10^{7})$,
$B=10(\log 3.1 +\log 10^7)$,
$B=10(\log 3.1+7)$,
$B=74.914$
(b). $B=10\log \frac{I}{I_0}=95$,
$\frac{95}{10}=\log I - \log 10^{-12}$,
$9.5=\log I +12$,
$-2.5=\log I$,
$I=10^{-2.5}$
(c). Without earbuds $I=3.1\times10^{-5}$,
With earbuds $I=10^{-2.5}$,
Therefore the ratio is, $10^{-2.5}:3.1\times10^{-5}=10^{2.5}:3.1$
