ページ3:

2-3 對數函數及其圖形:
*對數的比大小:
a=
© α= log 24, b = log, tr, c<log + 50, d = log to
α= log. 4. b = log, to, c=log, b, d= log &
71 3 4 2 4 7 1 b
'
© x 9 = log, 3, b = log 1 ½, c = log 12, d = log₁ =
先判斷正負,再雨雨比較
b7a,c<d
a=-log=3 / belog_3/co-log_2
2
bzdzuza
/ c=-log 2 / d = log₂ 2
...
*對數不等式:tips: 兩側真敬,必大於0(先做)
151 : log₁₂ 12x+b) < log (x²-x+2)
0 2 x + b 7 0 7 x7-6 = x7-3
x² + 270 70-2
④
條件
x+1
1
2
2 x 2 |
-372
© 2x++ b < xxx +2
x-4
④
-
④
x³-3x²-470 171
7 x74, x<-
函數的交點、方程式的實數解:
左二右
④:函數y=logo(0-1)與y=log:(一)兩圖形的交點座標
條件:31.3x29
1847-12272
74(x-1)=(8-95
v
7) 4x-4 = x²-18x+8)
7 x² - 2 x + 8 3 - 0 7 x = x 1 1 7
☆底數由小→大較好操作
ys log My
P3

ページ4:

2-3 對數函數及其圖形:
*指數方程式化為對數方程式:
:解方程式3+2=12x
tips: 同變為對數
log 3x+2 = log. 12x
⇒ (x+2) log 3 = log 12x
7 xlog3 +> logz = x log 12
7) 2log 3 = x (logiz-log3)
-7) > log } = xlog4
7) x = \logz x = log,} #
Flogz
*對數方程式:
(0,1)
x+1
=
132 : 4 4 3 7 1 1' 4*+ 1 128
log4 **1= log 12*
7) 2(x+1)_log==xlog 12
*) 2xlogz + 2 logz = x logiz
火
3) log== sloganl0912)
> > lo q 2 = x log + x =
-7) x = -logz = log. 2
-1093
Jologat-
(1,07
x
→對稱於x軸
- y = Ologat
y = log (0x)
:兩方程式圖形對稱軸
>
*對數函數的平移:y=1094 老換算
* 極值問題:
y= log x - log 47 y = log F2]
• Roxy, fool-log(x-xx+2)
x=0
(111)
X=4
Imax >
10917-17+2-1
147 max 111, mins 1
**=4 / max = log 10= |#
(012)] (4110) 1 x = 1 kg min = log 1=0#
Umin
↗
• 33 x x = 0, yo, 2x + y = 8, 2. log x + log y = 3
x+24
z
= √ 2xy = 8 2 x y = log by < log & }
下2
沪
P4