2016 · Q12
If 4ˣ2ʸ=128 and 3³ˣ3²ʸ-9ˣʸ=0,then the value of x + y can be equal to
Elementary MathematicsAlgebra
- A7
- B5
- C3
- D1
Explanation
4ˣ2ʸ = 2^{2x+y} = 128 = 2⁷ gives 2x+y = 7. From 3^{3x}·3^{2y} = 9^{xy} we get 3x+2y = 2xy. Substituting y = 7−2x yields 4x²−15x+14 = 0, so x = 2 or x = 7/4. Only x = 2 gives a listed sum: y = 3 and x+y = 5, option B.