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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!
You mean ##\log^{(3)} n = (\log n)^{(3)} = \log (\log(\log n))##In exactly the same way, cos^{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.
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.