✔ 最佳答案
1.下列敘述何者正確?(A) y=2^x+2的圖形對稱直線y=x,可以得到y=log<2>(x+2)的圖形Ans:對稱直線y=x: x,y互相交換可以獲得對稱點 => (x,y)->(y,x)y=2^x+2 => x=2^y+2 => 2^y=x-2兩邊取對數: log<2>(2^y)=log<2>(x-2)=> y=log<2>(x-2).....(X)
(B) y=2^x的圖形以X軸為基準，鉛直伸縮為3倍可以得到y=3*2^x的圖形與伸縮前全等Ans:(x,y) => (3x,y)y=2^x => y=2^(3x)=8*2^x.....ans=(X)
(C) y=log<4>(x^2)的圖形與y=log<2>x的圖形全等Ans:基本對數公式: log<a>b=log(b)/log(a)y=log<4>(x^2)=log(x^2)/log(4)=2*log(x)/2*log(2)=log(x)/log(2)=log<2>(x).....ans=(O)
2.不等式: 2*log<2>(x)-5+3*log<x>2<=0的解為?Ans:0>=2*log(x)/log(2)-5+3*log(2)/log(x)兩邊乘log(2)*log(x):0>=2*[log(x)]^2-5*log(2)*log(x)+3*[log(2)]^2=[2*log(x)-3*log(2)]*[log(x)-log(2)]=> log(2)<=log(x)<=(3/2)*log(2)
3.2^0.945+2^0.755>2^1.7=√(2^3.4)為何正確?Ans:算數平均數 > 幾何平均數.....兩數不相同 2^0.945+2^0.755 > 2*√(2^0.945*2^0.755)= 2*√(2^1.7)=√(2^2*2^1.7)=√(2^3.7)> √(2^3.4)=> 2^0.945+2^0.755 > 2^1.7
4.a=一萬元存入某銀行，已知定存的年利率為2%，每半年複利一次(r=1%)，試問需多少年後，本利何才能超過b=2萬元(log1.01=0.0043);第四題我算出的是:設x年 最後算出x>35 我的答案是36可是解答是35 ???Ans:b<=a(1+r)^x => log(b)<=x*log[a(1+r)]x>=log(b)/log(1+r).....a=1=log(2)/log(1.01)=0.30103/0.0043=70.007x/2>=35.035=36.....ans=取天花板整數
2014-01-29 07:27:30 補充：
修改1(B):
(x,y)->(x,3y)
y=2^x => 3y=2^x => y=(2^x)/3.....ans(X)
2014-01-29 07:30:37 補充：
代錯地點再修改1(B):
(x,y)->(x,3y)
y=2^x => Y=3*y=3*2^x .....ans(O)
