This is correct up to here although I think it would have been better to take the logarithm with respect to e, not 3, getting
2x= (x+ 3) ln(3) just because you can easily find a numerical value for log(3). But, as I say, what you have done is correct to this point.
But here you have gone wrong. Dividing the left side by "2x" leaves
Subtract from both sides to get and then, since "x" is in the denominator on the left, take the reciprocal of both sides: