Question

I need help with #3 of this problem. Thank you. The answer to #2 is d = log(I^20)

Answer 1

ANSWER

0.00018

EXPLANATION

First, we have to solve the equation from question 2 for I,

$d=\log (I^{20})$

Raise 10 to each of the sides of the equation,

$\begin{gathered} 10^d=10^{\log (I^{20})} \\ 10^d=I^{20} \end{gathered}$

And take the 20th root to both sides,

$I=10^{d/20}$

Now, we have to find the ratio of the intensity for the whisper and the intensity for the concert,

$\frac{I_{whisper}}{I_{concert}}=\frac{10^{45/20}}{10^{120/20}}=10^{(45-120)/20}=10^{-3.75}\approx0.00018$

The intensity of a whisper is 0.00018 times the intensity of a rock concert.