f4 maths (3 questions)

1) log√8﹣log√(4/5)
1) log√8–log√4/5
= log√23 – log√(8/10)
= log√23 –log√(23/10)
= 0.5log23 – 0.5log(23/10)
= 1.5log2 –1.5log2 + 0.5log10
= 1/2

2) (log9 + 3log2)/(log24﹣ log1/3)
= (log32+3log2)/(log(23x3)+log 3)
= (2log3+3log2)/(log23 +log3+log 3)
= (2log3+3log2)/(3log2 +2log3)
= (2log3+3log2)/(2log3 +3log2)
= 1

3) 1/2(log√216﹣3log√6 + log10)
= 1/2log√216﹣3/2log√6 + 1/2 log10
= log(2161/2)1/2﹣log(61/2)3/2 + 1/2 log10
= log(63/2)1/2﹣log63/4 + 1/2 (1)
= log63/4﹣log63/4 + 1/2
= 3/4 log6﹣3/4 log6+ 1/2
= 1/2

2007-11-21 23:29:39 補充：
個+1/2唔係次方第3題有顯示得唔清楚，= log6^(3/4)﹣log6^(3/4) + 1/2 = 3/4 log6﹣3/4 log6+ 1/2 = 1/2