I presume the question is 125^(8x - 2) = 150 ? If so, lg (has a base of 10) both sides of the equation, lg 125^(8x - 2) = lg 150 <Bring the power down to the left, using formulae of lg (a)^b = b × lg a> => (8x - 2) × lg 125 = lg 150 => (8x - 2) × lg 5^3 = lg 150 => 3(8x - 2) × lg 5 = lg 150 => (24x - 6) × lg 5 = lg 150 => 24x - 6 = lg 150 ÷ lg 5 => 24x = (lg 150 ÷ lg 5) + 6 => x = [(lg 150 ÷ lg 5) + 6] ÷ 24 => x ~ 0.379 (rounded off to 3 significant factors)