An NPN transistor operates as a common emitter amplifier, with a...

${A}_{v} \times \beta = {P}_{gain}$

$60 = 10\log_{10}\left(\dfrac{P}{{P}_{0}}\right)$
$P = {10}^{6} = {\beta}^{2} \times \dfrac{{R}_{out}}{{R}_{in}} = {\beta}^{2} \times \dfrac{{10}^{4}}{100}$
${\beta}^{2} = {10}^{4}$
$\beta = 100 = {10}^{2}$