# Small confusion regarding logarithmic formula

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1. Jan 29, 2015

### 22990atinesh

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

2. Jan 29, 2015

### Staff: Mentor

That's the one you want.

3. Jan 29, 2015

### Staff: 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.

4. Jan 29, 2015

### HallsofIvy

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!

Last edited by a moderator: Jan 30, 2015
5. Jan 31, 2015

### 22990atinesh

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

6. Jan 31, 2015

### Staff: Mentor

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.

7. Jan 31, 2015

### 22990atinesh

I know, I was just rechecking from you. :)