F.4maths對數函數

2014-05-26 3:02 am

試不用計數機求下列各式的值。
1. ㏒√0.1 - ㏒0.01

2. ㏒√x +3㏒x / ㏒x^3 - ㏒x^2

解下列各方程。
1. ㏒(3x+1) - ㏒(x-1) = ㏒5

2. ㏒(2x+6) - ㏒x =1

3. ㏒x^2 + ㏒2x =㏒16

4. ㏒5x+4㏒x = ㏒1215

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回答 (1)

LTW

2014-05-26 3:27 am

✔ 最佳答案

試不用計數機求下列各式的值。
1.
㏒√0.1 - ㏒0.01
=㏒10^(-1/2) - ㏒10^(-2)
=-1/2㏒10-(-2㏒10)
=-1/2+2
=3/2

2.
[㏒√x +3㏒x ]/ [㏒x^3 - ㏒x^2]
=[㏒x^(1/2) +3㏒x ]/ [㏒x^3 - ㏒x^2]
=[1/2㏒x +3㏒x ]/ [3㏒x - 2㏒x]
=[7/2 ㏒x]/ ㏒x
=7/2

解下列各方程。
1.
㏒(3x+1) - ㏒(x-1) = ㏒5
㏒[(3x+1)/(x-1)] = ㏒5
(3x+1)/(x-1) = 5
3x+1 = 5x-5
2x=6
x=3

2.
㏒(2x+6) - ㏒x =1
㏒[(2x+6)/x] =㏒10
(2x+6)/x=10
2x+6=10x
8x=6
x=3/4

3.
㏒x^2 + ㏒2x =㏒16
㏒[x^2 (2x)] =㏒16
2x^3 =16
x^3=8
x=2

4.
㏒5x+4㏒x = ㏒1215
㏒5x+㏒x^4 = ㏒1215
㏒[5x(x^4)] = ㏒1215
5x(x^4)=1215
5x^5=1215
x^5=243
x=3

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