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)(x-1)/(2x-11)(x−1)/(2x−11) = log_6 2
Now, since both sides of the equation have the same base logbase6log base 6logbase6, we can drop the logarithms and set the arguments equal to each other:
x−1x-1x−1/2x−112x-112x−11 = 2
Next, we can cross multiply to solve for x:
x−1x-1x−1 = 22x−112x-112x−11 x-1 = 4x - 2222 - 1 = 4x - x21 = 3xx = 7
Therefore, the solution to the logarithmic equation is x = 7.
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)(x-1)/(2x-11)(x−1)/(2x−11) = log_6 2
Now, since both sides of the equation have the same base logbase6log base 6logbase6, we can drop the logarithms and set the arguments equal to each other:
x−1x-1x−1/2x−112x-112x−11 = 2
Next, we can cross multiply to solve for x:
x−1x-1x−1 = 22x−112x-112x−11 x-1 = 4x - 22
22 - 1 = 4x - x
21 = 3x
x = 7
Therefore, the solution to the logarithmic equation is x = 7.