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

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28
Mar 20, 2016

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.

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