Answer
(a) $9$
(b) $9.542$
Work Step by Step
(a) We know that
$I=\frac{P}{\pi r^2}$
It is given that the distance decreases by a factor of three, so we replace $r$ by $\frac{1}{3}r$
$\implies I=\frac{P}{\pi (\frac{1}{3}r)^2}$
$\implies I=\frac{P}{\frac{\pi r^2}{9}}$
$\implies I=\frac{9P}{\pi r^2}$
Thus, the intensity increases by a factor of 9.
(b) We know that the intensity level is given as
$\beta=(10dB)log_{10}(\frac{I}{I_{\circ}})$
$\beta=(10dB)log_{10}(\frac{9P/ \pi r^2}{P/ \pi r^2})$
$\beta=(10dB)log_{10}(9)$
$\beta=9.542$
Thus, the intensity level increases by a factor of $9.542$
