續二次方程(15-18題)

15.
設 u = 2^(x + 2)

4^(x+2) + 2^(x+2) = 2
[2^(x+2)]^2 + 2^(x+2) - 2 = 0
u^2 + u - 2 = 0
(u -1)(u + 2) = 0
u = 1 或 u =-2
2^(x+2) = 1 或 2^(x+ 2) = -2(不合)
2^(x+2) = 2^0
x + 2 = 0
x = -2


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16.
設 u = 5^(1-x)

4[5^(1-x)] + 5^x = 9
4[5^(1-x)] + 5[5^(1-x)] = 9
9[5^(1-x)] = 9
5^(1-x) = 1
5^(1-x) = 5^0
1 - x = 0
x = 1


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17.
設 u = log(x-4)

[log(x-4)]^2 -3log(x-4) + 2=0
u^2 - 3u + 2 = 0
(u - 1)(u - 2) = 0
u = 1 或 u = 2
log(x-4) = 1 或 log(x-4) = 2
x - 4 = 10^1 或 x - 4 = 10^2
x = 14 或 x = 104


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18
3log^2(2x+1)^2 =[log^2(2x+1)^2] + 8
2[log^2(2x+1)^2] = 8
log^2(2x+1)^2 = 4
log(2x+1)^2 = 2 或 log(2x+1)^2 = -2
(2x+1)^2 = 10^2 或 (2x+1)^2 = 10^-2
2x + 1 = 10 或 2x + 1 = -10 或 2x + 1 = 1/10 或 2x + 1 = -1/10
x = 9/2 或 x = -11/2 或 x = -9/20 或 x = -11/20