Question

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

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

Answer 1

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`