# How to get the value of r when I have the value of r^² ( 1000 = r^2)?

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 $$\sqrt{1000}=10^{3/2}$$.