對數函數(20點)

4.
log4(3x - 2) = 2
log4(3x - 2) = 2log44
log4(3x - 2) = log44^2
3x - 2 = 16
3x = 18
x = 6


5.
3log4 + log2x = log768
log4^3 + log2x = log768
log64 + log2x = log768
log(64 * 2x) = log768
128x = 768
x = 6


6.
3log9 - logx = log3
log9^3 - logx = log3
log27 - logx = log3
log(27/x) = log3
27/x = 3
3x = 27
x = 9


8.
log(12x^2 - 20x) = log(5x - 12)
12x^2 - 20x = 5x - 12
12x^2 - 25x + 12 = 0
(3x - 4)(4x - 3) = 0
x = 4/3 或 x = 3/4

當 x = 4/3，log(5x- 12) = log(-16/3)，
負數的對數無定義，故不合，捨棄 x = 4/3。

當 x = 3/4，log(5x- 12) = log(-33/3)
負數的對數無定義，故不合，捨棄 x = 3/4

因此，此題無解。


= = = = =
12.
y = ka^x
log3y = log3(ka^x)
log3y = log3k + log3a^x
log3y = log3k + xlog3a ...... [i]

log3y = 5 + 2x ...... [ii]

比較 [i] 和[ii]:
log3k = 5 ...... [iii]
xlog3a = 2x ...... [iv]

由 [iii]:
k = 3^5
k = 243

由 [iv]:
xlog3a = 2x
log3a = 2
a = 3^2
a = 9

2011-06-12 16:50:58 補充：
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