Given that 2 to power x=8 to power (y+1) and 9 to power y=3 to power (x-9), the value of X+Y is ? (A)18 (B)21 (C)24 (D)27

Asked by Anubhav Sachan | 21st Oct, 2013, 06:45: PM

Expert Answer:

2x = 8y+1
=> 2x = (23)y+1
Since, base are same on both sides, x = 3(y+1)
or x = 3y + 3          ... (1)
 
And, 9y = 3x-9
(32)y = 3x-9
Since, base are same on both sides, 2y = x-9
or, x = 2y + 9         ... (2)
 
From (1) and (2), we have:
3y = 3 = 2y + 9
y = 6
 
From (1), x = 3y + 3 = 21
 
Thus. x + y = 21 + 6 = 27
 

Answered by  | 21st Oct, 2013, 10:48: PM

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