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)