I do not remember this from school anymore and I now I have to use the logarithm but the problem is that I do not know the base. I want to know the value of r but I only have the value of r^2.
2² = 2*2 and the inverse is log2(4) but in my case how do not have the value of the base. Thank you.
You really don't need the logarithm but a square root: $\sqrt{1000}$. However, presume for some reason you have to use logarithms somewhere(?!)
For positive $x$ it is true that $\sqrt{x}=x^{1/2}=a^{\frac12\log_ax}$ for any base $a\gt 0$ you choose. So, pick the base that is the easiest to work with. In this case, $1000=10^3$, i.e. $\log_{10}1000=3$ and so $a=10$ is a nice base to work with. Now it follows that $\sqrt{1000}=10^{3/2}$.