Solving this equation involves using two of the laws of exponents. The two laws are that
log(a b) = log(a) + log(b), and
log(ab) = b log(a)
You have 6x+1 =12x-3 so first take the log of both sides.
6x+1 =12x-3 and therefore log(6x+1) =log(12x-3 )
Now apply the second law above and then solve for x. You will be able to simplify the answer significantly if you use the first law above to evaluate log(12) and log(6).