CK-12-Calculus

6.2. Exponential and Logarithmic Functions http://www.ck12.org

logbx=logbby

=ylogbb

=y( 1 )

=y.

Thusy=f−^1 (x) =logbxis the inverse ofy=f(x) =bx.
This implies that the graphs offandf−^1 are reflections of one another about the liney=x.The figure below shows
this relationship.

Similarly, in the special case when the baseb=e,the two equations above take the forms

y=f(x) =ex

and

f−^1 (x) =lnx.

The graph below shows this relationship: