# Finding unknown in log equation I was given a log equation: D=10log(I/I_0) I is the unknown in this case, I_0=10^(−12) and D=89.3.

Finding unknown in log equation
I was given a log equation:
$D=10\mathrm{log}\left(I/{I}_{0}\right)$
$I$ is the unknown in this case, ${I}_{0}={10}^{-12}$ and $D=89.3$
I did the following steps:

I'm not quite sure how to isolate I after step 3, and I'm also unsure if dividing $89.3/10$ is correct as well. So how can I find the unknown ($I$)?
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Luna Wells
Yes you are on the right track. For logarithms we have
${\mathrm{log}}_{a}y=x\phantom{\rule{thickmathspace}{0ex}}⟺\phantom{\rule{thickmathspace}{0ex}}{a}^{x}=y$
Here's a tip: $\mathrm{log}\left(\frac{I}{{10}^{-12}}\right)=\mathrm{log}\left({10}^{12}I\right).$ So then we have
$8.93={\mathrm{log}}_{10}\left({10}^{12}I\right)\phantom{\rule{thickmathspace}{0ex}}⟹\phantom{\rule{thickmathspace}{0ex}}{10}^{8.93}={10}^{12}I\phantom{\rule{thickmathspace}{0ex}}⟹\phantom{\rule{thickmathspace}{0ex}}{10}^{8.93-12}=I\phantom{\rule{thickmathspace}{0ex}}⟹\phantom{\rule{thickmathspace}{0ex}}I={10}^{-3.07}$
###### Not exactly what you’re looking for?
sarahkobearab4
You're on the right way. You need to find the function f so that $f\left(log\left(x\right)\right)=x$
Hint
$\mathrm{\forall }x\in \mathbb{R},lo{g}_{a}\left({a}^{x}\right)=x,a\in \mathbb{R}$