SOLUTION: What is the relationship between the graphs of y = 2^x and x = 2^y

Question 227823: What is the relationship between the graphs of y = 2^x and x = 2^y
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you can solve y = 2^x easily enough.
In order to solve x = 2^y, you would have to solve for y.
x = 2^y if and only if y =

for example:

2^3 = 8

should equal 3

Convert to base of 10 in order to solve this using your calcultor.

Use the conversion formula of =

This becomes = 3.

To graph these equations, therefore:

y = 2^x can be graphed directly.

x = 2^y can be graphed by solving for y and getting y =

A graph of both of these equations looks like:

Since both these equations are reflections about the line y = x, this means that y = is the inverse function of y = 2^x.

The same graph with the line y = x added shows this.

In fact, in order to find the inverse function of y = 2^x, you would have to solve for x and then replace x with y and y with x.

You would wind up with the same equation.

y = 2^x if and only if x =

So when you solve for x, you get x =

When you replace y with x and x with y, you get:

y = which is the inverse equation of y = 2^x and is exactly the equation we got when we solved for y in order to be able to graph it.

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