Final answer:
To solve the exponential inequality (1/2)^2x + 1 = 4, subtract 1 from both sides, take the logarithm with base 1/2, and solve for x. The solution for x is approximately 1.585.
Step-by-step explanation:
To solve the exponential inequality (1/2)^2x + 1 = 4, we can first subtract 1 from both sides of the equation. This gives us (1/2)^2x = 3. Next, we can take the logarithm of both sides with base 1/2. This gives us 2x = log base 1/2 of 3. Finally, we divide both sides by 2 to solve for x, which gives us x = (1/2) * log base 1/2 of 3. The solution for x is approximately 1.585.