Small confusion regarding logarithmic formula

[22990atinesh]

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

 

[Doc Al]

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

That's the one you want.

 

[Mark44]

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]

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!

 

[22990atinesh]

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]

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.

$\log^3 n = (\log n)^3$

This is what I said.

 

[22990atinesh]

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. :)