To get rid of the pesky exponents at the top, you would turn both sides into a Logarithm with any base. Most of the time, we use base 10. So then, since it's a logarithm with an exponent, you turn the exponent into a coefficient, as you can do that. So it's turns into (2x-1)(Log(3)) = (x+1)(Log(7))
Then just divide both sides by Log(3) then distribute the right, then subtract like terms, and you got the answer.