換底公式 log~~急急急 help me!!!!!!!

用戶87356

2011-02-15 2:13 am

利用計算機,求下列各式的值.(答案須準確至3位有效數字)

2(a) log(右下方samll 2) 6 + log(右下方samll 2 ) 3

(b) log(右下方samll 3) 10 - log(右下方samll 3) 5

(c) (log{右下方samll 4} 9)(log{右下方samll 4 } 7)

(d) (log{右下方samll 2} 5)(log{右下方samll 5} 2)

(e) log(右下方samll 0.5 ) 1.5 / log(右下方samll 0.5) 2

回答 (2)

✔ 最佳答案

log_a(b)
( _a 是指以 a 為底數 )

2
a) log_2(6) + log_2(3)
= log_2(6 x 3)
= log_2(18)
= 4.17 (準確至 3 位有效數字)
http://www.google.com/search?hl=en&q=log%2818%29+%2F+log%282%29&aq=f&aqi=h1&aql=&oq=

b) log_3(10) - log_3(5)
= log_3(10 ÷ 5)
= log_3(2)
= 0.63 (準確至 3 位有效數字)
http://www.google.com/search?hl=en&q=log%282%29+%2F+log%283%29&aq=f&aqi=h1&aql=&oq=

c)
[log_4(9)][log_4(7)]
= 2.22 (準確至 3 位有效數字)
http://www.google.com/search?hl=en&q=log%289%29+x+log%287%29+%C3%B7+log%284%29+%C3%B7+log%284%29&aq=f&aqi=h1&aql=&oq=

d)
[log_2(5)][log_5(2)]
= log(5) x log(2) ÷ log(2) ÷ log(5)
= 1.00 (準確至 3 位有效數字)
http://www.google.com/search?hl=en&q=log%285%29+x+log%282%29+%C3%B7+log%282%29+%C3%B7+log%285%29&aq=f&aqi=h1&aql=&oq=

e)
log_0.5(1.5) ÷ log_0.5(2)
= log(1.5)/log(0.5) ÷ log(2)/log(0.5)
= log(1.5)/log(0.5) x log(0.5)/log(2)
= log(1.5)/log(2)
= 0.58 (準確至 3 位有效數字)
http://www.google.com/search?hl=en&q=log%281.5%29+%2F+log%282%29&aq=f&aqi=h1&aql=&oq=