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

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

1 Answer
Sep 23, 2017

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