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.
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.