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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 ##
That's the one you want.or ##\log^3 n = (\log n)^3 ##
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!
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.
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.You mean ##\log^{(3)} n = (\log n)^{(3)} = \log (\log(\log n))##
This is what I said.22990atinesh said:##\log^3 n = (\log n)^3##
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.