exponential functions

2010-02-22 7:52 am

1.
Given that R,x,y,z are integers and R>x>y>z.
If R,x,y,z satisfy the equation 2^R+2^x+2^y+2^z=165/8.
Find the value of R.

2.
Given that 48^x=2 and 48^y=3.
Find the value of 8^[(x+y)/(1-x-y)].

回答 (2)

用戶2053

2010-02-22 9:14 am

✔ 最佳答案

1)2^R+2^x+2^y+2^z=165/8

2^(R+3) + 2^(x+3) + 2^(y+3) + 2^(z+3) = 165

If R+3 = 2^6 , Max = 2^6 + 2^5 + 2^4 + 2^3 = 120 < 165 , so R+3 > 2^6

If R+3 = 2^8 = 256 > 165 , so R+3 < 2^8

Thus R+3 = 7

R = 4

2) 48^x = 2 ,

8^x = 2 / 6^x....(1)

&

48^y = 3

8^y = 3 / 6^y....(2)

(1)*(2) :

8^(x+y) = 6 / 6^(x+y)

8^(x+y) = 6 ^ (1 - x - y)

8^[(x+y)/(1-x-y)] = 6

2010-02-22 16:57:33 補充：
Q1)
If R+3 = 6 , Max = 2^6 + 2^5 + 2^4 + 2^3 = 120 < 165 , so R+3 > 6

If R+3 = 8 = 256 > 165 , so R+3 < 8

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天助

2010-02-22 8:03 am

1. (R, x, y, z)=(4, 2, -1, -3)
2. 6

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