Given 2^x=8^(y+1) and 9^y=3^(x-9), find the value of x+7.

Results 1 to 3 of 3

- Feb 26th 2007, 02:02 PM #1

- Joined
- Sep 2006
- Posts
- 75

- Feb 26th 2007, 03:14 PM #2

- Feb 27th 2007, 02:13 AM #3

- Joined
- Nov 2006
- Posts
- 136

2^x = 8^(y+1) is 2^x = 2^(3y+3) ---> x=3y+3.....(1)

9^y=3^(x-9) is 3^(2y) = 3^(x-9) ---> 2y=x-9......(2)

(x-3)/3 = y

substitute this into (2)

(2x - 6)/3 = x - 9

2x - 6 = 3x - 27

x = 21 (and y = 6)

therefore

x+7 = 28 -------> answer

we can check the value of x is correct by resubstitution

2^21 = 8^(7) = 2 097 152.