To solve this logarithmic equation, we can use the property of logarithms that states if log base a of b equals log base a of c, then b must equal c.

Therefore, we have:

5(4x - 32x) = 5(32x - 8)

Simplify the equation:

5(4x - 6x) = 5(6x - 8)

5(-2x) = 5(6x - 8)

-10x = 30x - 40

Combine like terms:

-10x - 30x = -40

-40x = -40

Divide by -40 to isolate x:

x = 1

Therefore, the solution to the equation log5(4x - 32x) = log5(32x - 8) is x = 1.