- #1

- 143

- 1

I've a small confusion about formula

##\log^3 n = \log \log \log n##

or ##\log^3 n = (\log n)^3 ##

##\log^3 n = \log \log \log n##

or ##\log^3 n = (\log n)^3 ##

You should upgrade or use an alternative browser.

- Thread starter 22990atinesh
- Start date

- #1

- 143

- 1

I've a small confusion about formula

##\log^3 n = \log \log \log n##

or ##\log^3 n = (\log n)^3 ##

##\log^3 n = \log \log \log n##

or ##\log^3 n = (\log n)^3 ##

- #2

Mentor

- 45,526

- 2,088

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

- #3

Mentor

- 37,231

- 9,395

- #4

Science Advisor

Homework Helper

- 43,008

- 974

It is not uncommon to put a an exponent in **parentheses** to indicate a repeated composition.

That is, [itex](log(x))^{(3)}[/itex] or [itex]log^{(3)}(x)[/itex] is "log(log(log(x)))".

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

That is, [itex](log(x))^{(3)}[/itex] or [itex]log^{(3)}(x)[/itex] 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:

- #5

- 143

- 1

parenthesesto indicate a repeated composition.

That is, [itex](log(x))^{(3)}[/itex] or [itex]log^{(3)}(x)[/itex] is "log(log(log(x)))".

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

^{2}(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##

- #6

Mentor

- 37,231

- 9,395

The above is what HallsOfIvy said. I haven't seen it, myself, but I have seen fYou mean ##\log^{(3)} n = (\log n)^{(3)} = \log (\log(\log n))##

This is what I said.22990atinesh said:##\log^3 n = (\log n)^3##

- #7

- 143

- 1

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

Share:

- Replies
- 4

- Views
- 1K

- Replies
- 28

- Views
- 2K

- Replies
- 2

- Views
- 1K

- Replies
- 3

- Views
- 424

- Replies
- 3

- Views
- 770

- Replies
- 18

- Views
- 1K

- Replies
- 3

- Views
- 679

- Replies
- 3

- Views
- 1K

- Replies
- 5

- Views
- 788

- Replies
- 16

- Views
- 1K