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

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Answer 1 · 2016-03-20T08:43:12

The inverse of $y = 2^{x}$ $y=2^x$ is $y = {log}_{2} x$ $y=log_2 x$

This is how to do it.
From the given $y = 2^{x}$ $y=2^x$

interchange the variables so that

$x = 2^{y}$ $x=2^y$
then solve for y:

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

take the logarithm of both sides with base $= 2$ $=2$

${log}_{2} x = {log}_{2} 2^{y}$ $log_2 x=log_2 2^y$

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

and

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

The graph of $y = 2^{x}$ $y=2^x$ and its inverse $y = {log}_{2} x$ $y=log_2 x$ . They are symmetric with the line $y = x$ $y=x$

graph{(y-2^x)(y-log x/log 2)(y-x)=0[-20,20,-10,10]}

God bless....I hope the explanation is useful.

How do you find the inverse of y=2xy = 2^x and is it a function?