To solve this inequality, we can start by rewriting the inequality with exponents instead of logarithms.

Given:
Log2x(0.125) ≥ log2(64x-1)

This can be rewritten as:
2^(log2x(0.125)) ≥ 2^(log2(64x-1))

Now, we can simplify the exponents using the property of logarithms that states:
If loga(b) = c, then a^c = b

Using this property, we get:
x ≥ 64x - 1

Next, let's solve for x:
x - 64x ≥ -1
-63x ≥ -1
x ≤ 1/63

Therefore, the solution to the inequality is x ≤ 1/63.