Given that (log_{3}(x – y) = 1) and (log_{3}(2x + y) = 2), find the value of x.
-
A.
1 -
B.
2 -
C.
3 -
D.
4
Correct Answer: Option D
Explanation
(log_{3}(x – y) = 1 implies x – y = 3^{1} = 3 …. (1))
(log_{3}(2x + y) = 2 implies 2x + y = 3^{2} = 9 ….. (2))
From (1), y = x – 3
From (2), y = 9 – 2x
(implies 9 – 2x = x – 3)
(9 + 3 = x + 2x = 3x)
(x = 4)