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

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#### Explanation

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#### Explanation:

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27
Mar 20, 2016

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

#### Explanation:

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

interchange the variables so that

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

$x = {2}^{y}$

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

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

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

and

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

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

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

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

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