How do I solve the equation for x? log(7x-2)-log(x-2)=1

How do I solve for x? i'm lost. I'm working on converting to the equivalent exponential forms and solving logarithmic equations? Please help..

How do I solve the equation for x? log(7x-2)-log(x-2)=1

[Remember that logs with the same base follow this law:
log (a) + log (b) = log (a * b)
log (a) - log (b) = log (a / b)]

therefore
log (7x - 2) - log (x - 2) = 1
log (7x - 2) / (x - 2) = 1
10^1 = (7x - 2) / (x - 2)
10 = (7x - 2) / (x - 2)
10 (x - 2) = 7x - 2
10x - 20 = 7x - 2
3x = 18
x = 6

Recall log(a)+log(b) = log(a/b), log(a^-1)=-log(a), and e^log(a)=a.

log(7x-2)-log(x-2)=log( (7x-2) / (x-2) )=1. Take exp of both sides.

e^(log(...))=e^1 = 7x-2/x-2. Multiply both sides by x-2.

(x-2)*e = 7x-2, now isolate x.

e*x - 7x = e*2 - 2, simplifying gives x(e-7)=2(e-1) so x=2(e-1)/(e-7)