How do you solve for x and y if log x - log y =2 and log x + log y = 0?

Question

5809 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-01T23:00:20

The point of intersection is $(10, 1/10)$ , assuming the logarithms are in base $10$ .

Isolate the $logx$ in equation $1$ .

$logx = 2 + logy$

Substitute for $logx$ in equation $2$ :

$2 + logy + logy = 0$

$2 + 2logy = 0$

$2(1 + logy) = 0$

$logy = -1$

$y = 10^-1$

$y = 1/10$

$:.logx = 2 + log(1/10)$

$logx - log(1/10) = 2$

$log(x/(1/10)) = 2$

$10x = 10^2$

$10x = 100$

$x = 10$

The solution point is $(10, 1/10)$ .

Hopefully this helps!