How do you simplify #Ln e^3#?

1 Answer
Aug 4, 2016

Answer:

#ln(e^3)=3#

Explanation:

By definition, #log_a(x)# is the value such that #a^(log_a(x)) = x#
From this, it should be clear that for any valid #a# and #b#, #log_a(a^b)=b#, as #log_a(a^b)# is the value such that #a^(log_a(a^b))=a^b#.

As the natural logarithm #ln# is just another way of writing the base-#e# logarithm #log_e#, we have

#ln(e^3) = log_e(e^3) = 3#