I'm trying to solve this question from mooculus and I get the wrong answer:
What I did:
$d=10\cdot \log_{10}(\frac I{I_0}) \\ \frac d{10} = \log_{10}(\frac I{I_0})\\ 10^\frac d{10}=\frac I{I_0}\\ I_0\cdot 10^\frac d{10} = I $
But then $ d^{-1}(85) = 10^{8.5} \cdot I_0 $ But the the answer is :
$ d^{-1}(85) = 3.2 \cdot 10^8 $ or approximately 320 million times the threshold sound.
What am I doing wrong ?
You're not doing anything wrong -- $10^{8.5}$ is approximately $3.2\times 10^8$, because $10^{0.5}=\sqrt{10} \approx 3.2$.
(The model answer is missing the $I_0$ factor from the result, which must be a typo).