To solve this equation, we can use the properties of logarithms.

First, we can combine the two logarithms using the property that states lg(a) - lg(b) = lg(a/b):

lg((3x-17)/(x+1)) = 0

Now, we can rewrite the equation in exponential form by raising both sides to the base 10:

10^0 = (3x-17)/(x+1)

1 = (3x-17)/(x+1)

Now we can cross multiply:

x + 1 = 3x - 17

And simplify:

1 + 17 = 3x - x

18 = 2x

x = 9

So the solution to the equation lg(3x-17) - lg(x+1) = 0 is x = 9.