Question

how to solve x for

12(log x)^2-14log(x)+2=0

i don't know how to factor out log and log x^2

Answer 1

perhaps you didn't recognize that this is really a quadratic equation, so let

y = logx
then your equation becomes
12y^2 - 14y + 2 = 0
6y^2 - 7y + 1 = 0
(6y-1)(y-1) = 0
then y = 1/6 or y = 1

then logx = 1/6
x = appr 1.468
or
logx = 1
x = 10