f.4 maths 20 marks

2010-08-11 11:03 pm
If log 2=a and log 3=b, express ln18/ln5 in terms of a and b.
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回答 (1)

2010-08-11 11:15 pm
✔ 最佳答案
log 18 = log ( 3 x 3 x 2) = log 3 + log 3 + log 2 = 2b + a
log 5 = log (10/2) = log 10 - log 2 = 1 - a
so answer is (a + 2b)/(1 - a).

2010-08-11 15:20:07 補充:
To be exact, ln 18 = log 18 to the base e = log 18 to the base 10 /log e to the base 10. Since it is divided by ln 5, so the log e to the base 10 cancelled out.


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