How do you find the inverse of $y = {log}_{2} 2 x$ $y=log_2 2x$ and is it a function?

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Answer 1 · 2016-10-21T18:46:46

$y = {log}_{2} (2 x)$ $y = log_2(2x)$

We obtain the inverse by switching the x and y values within the function.

$x = {log}_{2} (2 y)$ $x= log_2(2y)$

$2^{x} = 2 y$ $2^x = 2y$

$y = \frac{1}{2} (2^{x})$ $y= 1/2(2^x)$

$f^{- 1} (x) = \frac{1}{2} (2^{x})$ $f^-1(x) = 1/2(2^x)$

Hopefully this helps!

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