Are #lne# and #lne^x# the same?

1 Answer
Feb 16, 2017

Answer:

No

Explanation:

As #ln# is the natural logarithm then is is a logarithm using base #e# and therefore we can directly evaluate the two expressions as:

# ln e \ \= 1 #
# ln e^x = x #

These are clearly not the same.

If we could not directly evaluate then we can use the fact that for any base #b# then:

# log_b A = log_b B iff A=B #

and again it is clear that #e# and #e^x# are not identical.