Answer
The sound intensity level would be 72 decibels.
Work Step by Step
We can find the intensity of one professor talking.
$I_1= I_0~10^{\frac{\beta_1}{10}}$
$I_1= (10^{-12}~W/m^2)~10^{\frac{52}{10}}$
$I_1 = 1.585\times 10^{-7}~W/m^2$
We can find the intensity of 100 professors talking.
$I_2 = 100~I_1$
$I_2 = (100)(1.585\times 10^{-7}~W/m^2)$
$I_2 = 1.585\times 10^{-5}~W/m^2$
We can find the sound intensity level in decibels.
$I_2= I_0~10^{\frac{\beta_2}{10}}$
$10^{\frac{\beta_2}{10}} = \frac{I_2}{I_0}$
$log(10^{\frac{\beta_2}{10}}) = log(\frac{I_2}{I_0})$
$\frac{\beta_2}{10} = log(\frac{I_2}{I_0})$
$\beta_2 = 10~log(\frac{I_2}{I_0})$
$\beta_2 = 10~log(\frac{1.585\times 10^{-5}~W/m^2}{10^{-12}~W/m^2})$
$\beta_2 = 72~dB$
The sound intensity level would be 72 decibels.