log(x-2) +log8 (x-4) =log6 (x-1)

log(x-2) + log(x-4)/log8 = log(x-1)/log6

log[(x-2)(x-4)^(1/log8)] = log[(x-1)^(1/log6)]

(x-2)(x-4)^(1/log8) = (x-1)^(1/log6)
Ya got me.

Something tells me the problem was not as posted.

please solve it

To solve the equation log(x-2) + log8 (x-4) = log6 (x-1), we can use the properties of logarithms to simplify the equation and find the value of x.

Step 1: Combine the logarithms using the rules of logarithms.
Using the property log A + log B = log (A*B), we can rewrite the equation as:
log (x-2) * 8 (x-4) = log 6 (x-1)

Step 2: Rewrite the equation.
Using the property log A^n = n * log A, we can rewrite the equation as:
log [(x-2) * 8 (x-4)] = log (x-1)

Step 3: Remove the logarithm from both sides.
Since the logarithm function is one-to-one, we can remove the logarithm from both sides of the equation. This gives us:
(x-2) * 8 (x-4) = x-1

Step 4: Simplify and solve the equation.
Expand the expression on the left side:
8(x-2)(x-4) = x-1

Distribute the 8 across the terms:
8(x^2-6x+8) = x-1

Expand further by multiplying:
8x^2 - 48x + 64 = x - 1

Rearrange the equation to bring all the terms to one side:
8x^2 - 49x + 65 = 0

Now, we can solve this quadratic equation using factorization, completing the square, or the quadratic formula. Once we find the values of x, we can check if they satisfy the original equation.

Solving the above equation may involve complex numbers or irrational roots.