Home > Calculus > First Principles Example 3: square root of x

Is #(lnx)^2# equivalent to #ln^2 x#?

Is there even such a thing as #ln^2 x#?

Answer 1

Aurora Alvarado

Yes, but also see below

#ln^2 x# is simply another way of writing #(lnx)^2# and so they are equivalent.

However, these should not be confused with #ln x^2# which is equal to #2lnx#

There is only one condition where #ln^2 x = ln x^2# set out below.

#ln^2 x = ln x^2 -> (lnx)^2 = 2lnx#

#:. lnx * lnx = 2lnx#

Since #lnx !=0#

# lnx * cancel lnx = 2 * cancel lnx#

#lnx = 2#

#x =e^2#

Hence, #ln^2 x = ln x^2# is only true for #x=e^2#

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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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