對數函數(20點)

13.
(a)
log(25/27)
= log25 - log27
= log5^2 - log3^3
= 2log5 - 3log3
= 2s - 3t

(b)
log√6
= log6^(1/2)
= (1/2)log6
= (1/2)log(3 * 10 / 5)
= (1/2)(log3 + log10 - log5)
= (1/2)(s + 1 - t)


= = = = =
14.
(a)
logk(3) = 1/2
k^(1/2) = 3
[k^(1/2)]^2 = 3^2
k = 9

(b)
logk5 = -1/3
k^(-1/3) = 5
[k^(-1/3)]^(-3) = 5^(-3)
k = 1/125


= = = = =
log3√[27^(4k+2)/9^3k]
= log3[(3^3)^(4k+2)/(3^2)^3k]^(1/2)
= log3[3^(12k+6)/3^6k]^(1/2)
= log3[3^(12k+6-6k)]^(1/2)
= log3[3^(6k+6)]^(1/2)
= log3[3^(3k+3)]
= (3k+3)log33
= 3k+3

2011-06-12 16:51:26 補充：
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