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

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- Feb 26th 2007, 03:02 PMceasar_19134Given 2^x=8^(y+1)...
Given 2^x=8^(y+1) and 9^y=3^(x-9), find the value of x+7.

- Feb 26th 2007, 04:14 PMPlato
- Feb 27th 2007, 03:13 AMchogo
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.