What is the inverse of $y = {log}_{2} (2 x)$ $y= log_2(2x)$ ?

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Answer 1 · 2015-10-27T20:30:59

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

You can use the definition of log:
( ${log}_{a} x = b \to x = a^{b}$ $log_ax=b->x=a^b$ ) and get:

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

so that:
$x = \frac{2^{y}}{2} = \frac{2^{y}}{2^{1}} = 2^{y - 1}$ $x=2^y/2=2^y/2^1=2^(y-1)$
That we can write:
$y = 2^{x - 1}$ $color(red)(y=2^(x-1))$

graph{2^(x-1) [-11.25, 11.245, -5.63, 5.62]}

What is the inverse of y=log2(2x)y= log_2(2x) ?