Home » If (5^{(x + 2y)} = 5) and (4^{(x + 3y)} = 16), find (3^{(x +…

If (5^{(x + 2y)} = 5) and (4^{(x + 3y)} = 16), find (3^{(x +…

If (5^{(x + 2y)} = 5) and (4^{(x + 3y)} = 16), find (3^{(x + y)}).

  • A.
    7
  • B.
    1
  • C.
    3
  • D.
    27
Correct Answer: Option B
Explanation

(5^{(x + 2y)} = 5)

∴ x + 2y = 1…..(i)
(4^{(x + 3y)} = 16 = 4^2)

x + 3y = 2 …..(ii)
x + 2y = 1…..(i)
x + 3y = 2……(ii)
y = 1
Substitute y = 1 into equation (i) 

(x + 2y = 1 implies x + 2(1) = 1)

(x + 2 = 1 implies x = -1)

(therefore 3^{(x + y)} = 3^{(-1 + 1)})

(3^{0} = 1)