How do you simplify #lne^4#?

Answer 1

#4#

You may put any power in the argument before the #ln#: #lne^4=4lne# (this goes for #log#'s to any base)

Then since #e# is the base of the #ln#-function (#lnx=log_e x#), it follows that: #lne=log_e e=1#, just as #log_10 10=1#

So: #lne^4=4*lne=4*1=4#

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Answer 2

James Allen

To simplify ln(e^4):

ln(e^4) = 4

The natural logarithm of e raised to any power is simply equal to that power. Therefore, ln(e^4) simplifies to 4.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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