To solve this logarithmic equation, we can first combine the two logarithms on the left side using the product rule of logarithms:

log2(4-x) + log2(5) = log2(x-1)
log2((4-x)*5) = log2(x-1)
log2(20-5x) = log2(x-1)

Now, remove the logarithms and set the expressions equal to each other:

20 - 5x = x - 1

Combine like terms:

20 + 1 = x + 5x
21 = 6x

Divide by 6:

x = 21/6
x = 3.5

Therefore, the solution to the logarithmic equation is x = 3.5.