text: how do i solve log x (logx^2) + log x^9 -5 =0?   (log x)(log x^2) + log x^9 - 5 = 2 (log x)^2 + 9 log x - 5  let t=log x then, 2 t^2 + 9t -5 =0 is just a simple quadratic function factor: (2t-1)(t+5) = 0 hence, t=1/2 or t=-5  since t=log x, and a log function is never negative, we get t=log x = 1/2 so, x = exp(1/2) = 1.6487