Log_6(x-1)-log_6(2x-11)=log_6 2

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To solve this logarithmic equation, we can combine the two logarithms on the left side using the quotient rule for logarithms:

log_6((x-1)/(2x-11)) = log_6 2

Now, since both sides of the equation have the same base (log base 6), we can drop the logarithms and set the arguments equal to each other:

(x-1)/(2x-11) = 2

Next, we can cross multiply to solve for x:

(x-1) = 2(2x-11)
x-1 = 4x - 22
22 - 1 = 4x - x
21 = 3x
x = 7

Therefore, the solution to the logarithmic equation is x = 7.