4log2x−3≤−7

Sure, let's solve the inequality step by step:

1. First, isolate the logarithmic expression by adding 3 to both sides of the inequality:

   4log2x ≤ -7 + 3 4log2x ≤ -4

2. Next, divide both sides by 4:

   log2x ≤ -1

3. Now, to remove the logarithm, we can use the property of logarithms that states b^logb(a) = a. In this case, we raise 2 (the base of the logarithm) to the power of both sides:

   2^(log2x) ≤ 2^(-1) x ≤ 1/2

So, the solution to the inequality 4log2x - 3 ≤ -7 is x ≤ 1/2.