1)log6 2x-log6 2 = log6(2x-1)

First, we can simplify the left side of the equation using the rule that states that the logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator:

log6(2x) - log6(2) = log6(2x/2) = log6(x)

Substituting this into the original equation, we get:

log6(x) = log6(2x-1)

Now we can use the fact that if two logarithms with the same base are equal, then their arguments must be equal as well. Therefore, we have:

x = 2x - 1

Solving for x, we get:

x = 1

Therefore, the solution to the equation is x = 1.