To simplify this expression, we will first use the properties of logarithms:

log 1/2 (1/8) - log 1/2 (1/4) = log 1/2 (1/8 / 1/4)

Next, simplify the expression inside the logarithm:

log 1/2 (1/8 / 1/4) = log 1/2 (1/8 * 4/1) = log 1/2 (4/8) = log 1/2 (1/2)

Now, we can see that the argument of the logarithm is 1/2 itself, which means the result is 1:

log 1/2 (1/2) = 1

Therefore, the simplified expression is 1.