20 點(easy) . 哭求3題 f. 3 index數

(a) 2 x 3^(n+2) - 5 x 3^(n+1)/5 x 3^n + 4 x 3^(n+1)
=2x3^2x3^n-5x3x3^n/5x3^n+4x3x3^n
=(3x3^n)/(17x3^n)
=3/17

(c) arrange 5^100, 25^56, 125^25, 625^20 in descending order
5^100
25^56=5^112
125^25=5^75
625^20 =5^80
所以25^56> 5^100> 625^20> 125^25

2010-09-13 20:02:17 補充：
(B)題等等

2010-09-14 16:28:38 補充：
b題有無打錯問題?

Are you sure the equation b is correct?

(a) 2 x 3^(n+2) - 5 x 3^(n+1)
___________________
5 x 3^n + 4 x 3^(n+1)

= 2 x 3^n x 3^2 -5 x 3^nx3
____________________
5 x 3^n + 4 x 3^n x 3

= 18-15
_____
5+3

= 3
_
8//

(b) 9a^(2n+4) - 27a^(3n+3)
__________________
9a^(3n-1) - 3a^(2n)

幫你唔到

(c) arrange 5^100, 25^56, 125^25, 625^20 in descending order
5^100=5^100
25^56 = 5^112
125^25 = 5^75
625^20 = 5^80
25^56 > 5^100 > 625^20 >125^25

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5^100, 25^56, 125^25, 625^20

5^100 = ( 5^4 ) ^ 25

= 625 ^ 25

25 ^ 56

= 5 ^ 112

= ( 5 ^ 4 ) ^ 28

= 625 ^ 28

125 ^ 25

= 5 ^ 75

= ( 5 ^ 4 ) ^ 18 x 5 x 5 x 5

= 625 ^ 18 x 5 ^ 3

so,

25^56 > 5 ^ 100 > 625 ^ 20 > 125 ^ 25