Answer
To reduce the intensity by a factor of 2.0, the intensity level would have to be $97~dB$
Work Step by Step
Let $\beta_1 = 100.0~dB$ and suppose that $I_2 = \frac{I_1}{2.0}$. We can find the intensity level $\beta_2$:
$\beta_1-\beta_2 = 10~log~\frac{I_1}{I_0}-10~log~\frac{I_2}{I_0}$
$\beta_1-\beta_2 = 10~log~\frac{I_1}{I_2}$
$\beta_1-\beta_2 = 10~log~\frac{I_1}{I_1/2.0}$
$\beta_1-\beta_2 = 10~log~2.0$
$\beta_2 = \beta_1 - 10~log~2.0$
$\beta_2 = 97~dB$
To reduce the intensity by a factor of 2.0, the intensity level would have to be $97~dB$.
