# I need to sort out the theta complexity for lg(n^(1/2)) [closed]

Can you help me find the theta complexity for lg(n^(1/2))?

• $\Theta(\log n^{42})$. Also $\Theta(\log n^c)$ for any constant $c>0$ of your choice. Jun 16 at 17:12

$$log(n^{\frac{1}{2}}) = \frac{1}{2}log(n) = \theta(log(n))$$.

More formally, there exists constants $$c1$$,$$c2$$ such that:

$$c1⋅\frac{1}{2}log(n)≤log(n)≤c2⋅\frac{1}{2}log(n)$$

$$\lg(\sqrt n)=\Theta(\lg(\sqrt n)).$$
This is true as of $$n=1$$ with constants $$1$$.
$$\lg(\sqrt n)=\Theta\left(\sum_{k=1}^n\frac1k\right).$$
(Holds as of $$n=2$$ with constants $$0.2$$ and $$1$$.)