# Small confusion regarding logarithmic formula

I've a small confusion about formula
##\log^3 n = \log \log \log n##
or ##\log^3 n = (\log n)^3 ##

Doc Al
Mentor
or ##\log^3 n = (\log n)^3 ##
That's the one you want.

Mark44
Mentor
In exactly the same way, cos2(x) does not mean cos(cos(x)), but rather it means cos(x) * cos(x) = (cos(x))2. The exponent indicates repeated multiplication, not repeated function composition.

HallsofIvy
Homework Helper
It is not uncommon to put a an exponent in parentheses to indicate a repeated composition.
That is, $(log(x))^{(3)}$ or $log^{(3)}(x)$ is "log(log(log(x)))".

Unfortunately, that is also often used to indicate the third derivative so you must be careful to state which!

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It is not uncommon to put a an exponent in parentheses to indicate a repeated composition.
That is, $(log(x))^{(3)}$ or $log^{(3)}(x)$ is "log(log(log(x)))".

Unfortunately, that is also often used to indicate the third derivative so you must be careful to state which!
In exactly the same way, cos2(x) does not mean cos(cos(x)), but rather it means cos(x) * cos(x) = (cos(x))2. The exponent indicates repeated multiplication, not repeated function composition.

You mean ##\log^{(3)} n = (\log n)^{(3)} = \log (\log(\log n))##
##\log^3 n = (\log n)^3##

Mark44
Mentor
You mean ##\log^{(3)} n = (\log n)^{(3)} = \log (\log(\log n))##
The above is what HallsOfIvy said. I haven't seen it, myself, but I have seen f(3), with parentheses around the exponent, to indicate the third derivative.
22990atinesh said:
##\log^3 n = (\log n)^3##
This is what I said.

The above is what HallsOfIvy said. I haven't seen it, myself, but I have seen f(3), with parentheses around the exponent, to indicate the third derivative.

This is what I said.
I know, I was just rechecking from you. :)