Solve for x: log5(x-2)+log8(x-4) = log6(x-1). I do not have any idea on this topic.

I am not sure if the 5 , 8 , and 6 are bases of the logs

or just multipliers.
Let's hope they are just multipliers, or else it would be a terrible terrible mess

by the laws of logs
log5(x-2)+log8(x-4) = log6(x-1)
log [40(x-2)(x-4)] = log 6(x-1)
anti-log it

40(x^2 - 6x + 8) = 6x-6
40x^2 - 240x + 320 - 6x + 6 = 0
40x^2 - 246x + 326 = 0
20x^2 - 123x + 163 = 0
by the formula
x = (123 ± √2089)/40
= 4.2176 or 1.9324 , but from the original equation , x > 4

so x = 4.2176

I tested the answer, it works

To solve the given equation log5(x-2) + log8(x-4) = log6(x-1), we can use the properties of logarithms.

Step 1: Combine the logarithms using the properties of logarithms, specifically the product rule.
log5(x-2) + log8(x-4) = log6(x-1)

Step 2: Apply the product rule to combine the logarithms.
log5[(x-2)(x-4)] = log6(x-1)

Step 3: Simplify and rewrite the equation.
log5[(x^2 - 6x + 8)] = log6(x-1)

Step 4: Use the property of logarithms to eliminate the logarithms by taking the exponent of the same base on both sides.
5^(log5[(x^2 - 6x + 8)]) = 5^(log6(x-1))

Step 5: Simplify and rewrite the equation.
x^2 - 6x + 8 = (x-1)^5

Step 6: Expand the expression on the right side of the equation.
x^2 - 6x + 8 = x^5 - 5x^4 + 10x^3 - 10x^2 + 5x - 1

Step 7: Rearrange the equation to bring all terms to one side.
x^5 - 5x^4 + 10x^3 - 10x^2 + 5x - 1 - x^2 + 6x - 8 = 0

Step 8: Combine like terms.
x^5 - 5x^4 + 10x^3 - 11x^2 + 11x - 9 = 0

Step 9: Unfortunately, this equation does not have a simple algebraic solution. You will need to use numerical methods or graphing to approximate the value of x that satisfies this equation.