Dear friends, Please read our latest blog post for an important announcement about the website. ❤, The Socratic Team

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

Then teach the underlying concepts
Don't copy without citing sources
preview
?

Write a one sentence answer...

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

Describe your changes (optional) 200

28
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.

##### Just asked! See more
• 16 minutes ago
• 17 minutes ago
• 17 minutes ago
• 23 minutes ago
• 2 minutes ago
• 14 minutes ago
• 14 minutes ago
• 14 minutes ago
• 15 minutes ago
• 16 minutes ago
• 16 minutes ago
• 17 minutes ago
• 17 minutes ago
• 23 minutes ago