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

Question

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.

Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. — José Carlos Santos, Aug 23 '20 at 12:14

score 1 · Accepted Answer · answered Aug 23 '20 at 12:13

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

thank you. I was completly miles away. – Kaspacainoombro Aug 23 '20 at 12:32 — Kaspacainoombro, Aug 23 '20 at 12:32

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

1 Answers1