0
$\begingroup$

I am learning about algorithmic complexities and I have this claim which I need to prove or disprove: $f(n)$ and $g(n)$ are asymptotically positive functions, if $f(n)=\Theta(g(\log(n))$ then $f(n)=\Theta(\log(g(n)))$. Is it true?

$\endgroup$
1
  • 1
    $\begingroup$ No. I'm sure you can find a counterexample if you try a few functions. $\endgroup$ Commented Apr 6, 2020 at 18:41

1 Answer 1

2
$\begingroup$

An obvious counter example is $g(n) = \sqrt{n}$. If $f(n) = \Theta(\sqrt{\log n})$, you can't conclude that $f(n) = \Theta(\log{\sqrt{n}}) = \Theta(\log{n})$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.