急啊~求對數的運算!!20點

1.
log2 (1/2) + log2 (2/3) + log2­ (3/4) + ......+ log2 (126/127) + log2(127/128)
= log2 [(1/2) x (2/3) x (3/4) x ...... x (126/127) x (127/128)]
= log2 (1/128)
= log2 2⁻⁷
= -7 log22
= -7 x 1
= -7


2.
2 log (25/6) + 6 log(2/3) - 4 log(10/9)
= log (25/6)² + log(2/3)⁶ - log(10/9)⁴
= log (625/36) + log (64/729) - log(10000/6561)
= log [(625/36) x (64/729)] - log (10000/6561)
= log [(40000/26244)] - log (10000/6561)
= log [(10000/6561)] - log (10000/6561)
= 0

2013-12-31 01:48:19 補充：
2. 另解

2 log (25/6) + 6 log(2/3) - 4 log(10/9)

= 2 log 25 - 2 log 6 + 6 log2 - 6 log 3 - 4 log 10 + 4 log 9

= 2 log 5² - 2 log (2 x 3) + 6 log2 - 6 log 3 - 4 log (2 x 5) + 4 log 3²

= 4 log 5 - 2 log 2 - 2 log 3 + 6 log2 - 6 log 3 - 4 log 2 - 4 log 5 + 8 log 3

= 0

= 4 log 5 - 2 log 2 - 2 log 3 + 6 log2 - 6 log 3 - 4 log 2 - 4 log 5 + 8 log 3
這裡是前後分別算嗎?