Verified answer

Remember that the difference of two logs (with the same base) is the same as the log of the quotient.

So we turn the left side into:

log3 [(x-1)/(x-5)]

This gives us:

log3 [(x-1)/(x-5)] = 1

Now we just raise 3 to the power of both sides:

(x-1)/(x-5) = 3

And it's good ol' algebra from here.

Multiply both sides by x-5:

x-1 = 3x-15

Add 15 to both sides:

x+14 = 3x

Subtract x from both sides:

14 = 2x

Divide both sides by 2:

7 = x

Side note: just as the difference of two logs (with the same base) is the log of the quotient, the sum of two logs (with the same base) is the log of the product.

I agree with Conan!