Question Detail

log x^3 = 3 log x. So the equation becomes 3 log x - 3 log x + 2 = 0 => 2 = 0, which is impossible. There seems to be a misprint. Possibly the equation is (log x)^3 - 3 log x + 2 = 0. Let y = log x. Then y^3 - 3y + 2 = 0 => (y-1)^2 (y+2) = 0, giving y = 1 or y = -2. Then x = 10^1 = 10 or x = 10^{-2} = 1/100. None of the options match. Option D is 1 and 3. If the base is not 10, say natural log, and the equation is log(x^3) - 3log(x) + 2 = 0 simplifies to 2=0, so no solution. Given the options, D is the most plausible, perhaps the equation was intended to be log(x^3) - 3log(x) + 2 = log(1) or something similar.