Which function is the inverse of y=2^x

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]}