幾條關於log的問題

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2011-04-03 3:07 am

圖片參考：http://imgcld.yimg.com/8/n/HA00571484/o/701104020093413873405650.jpg

幾條關於log的問題，要清楚列式步驟。

題目要求：不使用計算機求以上各值.

回答 (1)

用戶2053

2011-04-03 3:43 am

✔ 最佳答案

1)log12 8 + 1.5log12 3= log12 (4^1.5) + 1.5log12 3= 1.5 log12 4 + 1.5 log12 3= 1.5 (log12 4 + log12 3)= 1.5 log12 12= 1.5
2)log√(2/7) - log(1/7) + (1/2)log(5/7)= log [√(2/7) / (1/7) * √(5/7)]= log [√10/7 / (1/7)]= log √10= log 10^(1/2)= 1/2
3)log4 (1/2)= log4 (1/√4)= log4 4^(-1/2)= - 1/2
4)log4 96 - log3 / log4= log4 96 - log4 3= log4 (96/3)= log4 32= log4 (4^2.5)= 2.5
5)2 + log3 0.75 + log3 (2/3)²= 2 + log3 (0.75 * (2/3)²)= 2 + log3 (1/3)= 2 + log3 (3^-1)= 2 + (- 1)= 1

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