How do you find the inverse of #f(x) =10^x#?

1 Answer
Sep 29, 2015

#f^(-1)(x)=logx#

Explanation:

By definition, #y=f^(-1)(x)ifff(y)=x#
#iff 10^y=x#
We can now take log base 10 on both sides and use laws of logs to yield
#y=log_10x#

I will also show the graphs of both f and its inverse for clarity.

graph{10^x [-6.37, 6.12, -2.67, 3.57]}

graph{logx [-2.26, 6.514, -2.257, 2.126]}