Explanation

Set t = 3^(x−1); then 3^(3−x) = 3²/3^(x−1) = 9/t, so the equation becomes t + 9/t = 6. Multiplying by t gives t² − 6t + 9 = 0, i.e. (t − 3)² = 0, so t = 3. Thus 3^(x−1) = 3, giving x − 1 = 1 and x = 2. Substituting, 2^(x−1) + 2^(3−x) = 2¹ + 2¹ = 4. The answer is (A) 4.