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標題:

exponential functions

發問:

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)].

最佳解答:

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此文章來自奇摩知識+如有不便請留言告知

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

其他解答:

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