# Small confusion regarding logarithmic formula

• 22990atinesh

#### 22990atinesh

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

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

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.

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##

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. :)