log數,對數題目(10分)

2011-02-12 10:53 am
我想問如果兩個log數的底不一樣,乘起, 如下:

1.)log(2)5 * log(5)2

2.)log(3)5 * log(5)7 * log(7)9!!! 括號內的數字是log數的底!!!


唔該曬!!!:)

回答 (3)

2011-02-12 5:57 pm
✔ 最佳答案
我想問如果倆的log數的底不一樣,乘起
Sol

圖片參考:http://imgcld.yimg.com/8/n/AC06500977/o/701102120019913873379890.jpg


2011-02-12 09:58:25 補充:
1.
log(2)5*log5(2)=log(2)2=1
2011-02-13 4:10 am
1.)log(2)5 * log(5)2
Sol
log(2)5*log(5)2
=(log5/log2)*(log2/log5)
=1

2.)log(3)5 * log(5)7 * log(7)9
Sol
log(3)5 * log(5)7 * log(7)9
=(log5/log3)*(log7/log5)*(log9/log7)
=log9/log3
=2
2011-02-12 12:39 pm
1. = log5 / 1og2 x log2 / log 5 = log(5+2) / log (2+5) = 1

2. = (log5 / log3) x (log7 / log5) x (log9 / log7) = log9 / log3 = 2


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