solve the exponential equation125^8x-2=150

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)

Hope this helps! :)