# What is the inverse of y=log( -3x) +2? ?

Nov 12, 2015

Given:
$y = \log \left(- 3 x\right) + 2$

$\log \left(- 3 x\right) = y - 2$

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Consider the case of$\text{ } {\log}_{10} \left(6\right) = b$
This means that ${10}^{b} = 6$

When you see just $\text{ "log("of something") " }$ it is understood to mean log to base 10.
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So now we have ${10}^{y - 2} = \left(- 3\right) x$

Thus we have $x = - \frac{{10}^{y - 2}}{3}$

Now interchange the variables of $x$ and $y$ to give:

$y = - \frac{{10}^{x - 2}}{3}$

If you we to incorporate logs now you would end up with $\log \left(y\right) =$ which is not the same as $y =$