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

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

1 Answer
Sep 23, 2017

Answer:

Yes, but also see below

Explanation:

#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#