Solve for x: log₂(x + 3) + log₂(x − 1) = 3.
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- Let distance be d. Time to B = d/60, time to return = d/40.
- Total distance = 2d. Total time = d/60 + d/40 = (2d + 3d)/120 = 5d/120 = d/24.
- Average speed = total distance / total time = 2d / (d/24) = 48 km/h.
- Combine logs: log₂[(x + 3)(x − 1)] = 3 → (x + 3)(x − 1) = 2³ = 8.
- Expand: x² + 2x − 3 = 8 → x² + 2x − 11 = 0.
- Use quadratic formula: x = [−2 ± √(4 + 44)] / 2 = [−2 ± √48]/2 = [−2 ± 4√3]/2 = −1 ± 2√3.
