# What is the inverse of log (x^2/2)-3log(x) ?

Mar 26, 2016

$x = {10}^{- y} / 2$, , where y is the given function.

#### Explanation:

Let $y = \log \left({x}^{2} / 2\right) - 3 \log \left(x\right)$

= $\log \left({x}^{2}\right) + \log \left({x}^{- 3}\right) + \log \left({2}^{- 1}\right)$

= $\log \left({\left(2 x\right)}^{- 1}\right)$.

Inversely, ${\left(2 x\right)}^{- 1} = {10}^{y}$. So, $x = {10}^{- y} / 2$