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MATHS (指數與對數函數)

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2.設 log2 = a , log 3 = b , log7 = c。把下列各數以a , b , c 表示 (a) log 42 (b) log 105 (c) log 375 (d) log √60 (e) log6√42 (f) log (sin pie/3)

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2.設 log2 = a , log 3 = b , log7 = c。把下列各數以a , b , c 表示 (a) log 42 =log(2*3*7) =log(2)+log(3)+log7) =a+b+c (b) log 105 =log(3*5*7) =log(3*10/2*7) =log(3)+log(10)-log(2)+log(7) =1-a+b+c (c) log 375 =log(3*5*5*5) =log(3*10*10*10/2/2/2) =log(3)+log(10)+log(10)+log(10)-log(2)-log(2)-log(2) =3-3a+b (d) log √60 =(1/2)log(60) =(1/2)log(2*3*10) =(1/2)[log(2)+log(3)+1] =(1/2)(1+a+b) (e) log6√42 =(1/6)log(2*3*7) =(1/6)[log(2)+log(3)+log(7)] =(1/6)(a+b+c) (f) log (sin pie/3) =log(√3/2) =log(√3)-log(2) =(1/2)log(3)-log(2) =(1/2)b-a

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