1. ## Ln X

Does (LN x)^3 = LN^3 x ?

2. Originally Posted by kid funky fried
Does (LN x)^3 = LN^3 x ?
It depends on the context. $\displaystyle ln^3(x)$ can either mean $\displaystyle ln(x) \cdot ln(x) \cdot ln(x)$ or it can mean $\displaystyle ln(ln(ln(x)))$, which are two very different things. I typically use it as the former expression, but there are cases where you would want to use it for the latter.

Edit: By the way, note that the function is ln(x), not Ln(x) or LN(x). Mathematics (and Physics, and Engineering, and...) is a "case-sensitive" field of study.

-Dan

3. Originally Posted by kid funky fried
Does (LN x)^3 = LN^3 x ?
It's not notation I'd use, but yes, I suppose it does.

As long as you realise it's NOT LN (x^3)

4. ## thx

thx.
I will make sure to use the proper case next time.
My answer book was using both expressions so i was beginning to wonder.

5. In may be helpful to note that the notation $\displaystyle \left( {\ln \left( x \right)} \right)^n$ is used by almost all computer algebra systems.