How do you evaluate #e^(lny)#?

1 Answer
Daniel L.
Dec 16, 2016

This expression evaluates ro #y# for every positive real number #y#. See explanation.

Explanation:

#f(y)=e^y# and #g(y)=lny# are inverse functions, so both compositions: #e^lny# and #lne^y# evaluate to #y# in all their domains.

Since #lny# is only defined for #y>0# the domain of the givenexpression is also #y>0#.

So the expression #e^lny# is equal to #y# for all positive real numbers #y#

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