How do you find the inverse of $y = {log}_{2} 2 x$ $y=log_2 2x$ ?

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Answer 1 · 2018-05-03T09:31:43

$y = 2^{x - 1}$ $y=2^(x-1)$

When finding the inverse function of something, you have to switch the x and y around

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

Now all you have to do is to make y the subject

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

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

$y = \frac{2^{x}}{2}$ $y=2^x/2$

$y = 2^{x - 1}$ $y=2^(x-1)$

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