log(1000 x^2)=(log x)^2

Like this:


log(1000 x^2) = [log(x)]^2 \\
log(1000) + 2 log(x) = [log(x)]^2 \\
(log(x))^2 - 2 log (x) - log(1000) = 0


Now use the quatratic equation to solve for log(x), and from that you can determine x.