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

1 Answer

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.