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www.yinhe910.com:高一数学人教A版必修一《2.2.2 对数函数及其性质的应用 第二课时》课件_图文

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2.2.2对数函数 及其性质
第二课时 对数函数及其性 质的应用

复习引入
1. 对数函数的定义: 函数y=logax (a>0且a≠1)叫做

对数函数,定义域为(0,+∞),
值域为(-∞,+∞).

2. 对数函数的性质:
a>1 0<a<1

图 象

性 质

2. 对数函数的性质:
a>1 0<a<1
x

图 象

y
O

性 质

2. 对数函数的性质:
a>1 0<a<1
y

图 象

y
O

x

O

x

定义域:(0, +∞);

性 质

2. 对数函数的性质:
a>1 0<a<1
y

图 象

y
O

x

O

x

定义域:(0, +∞); 值域:R

性 质

2. 对数函数的性质:
a>1 0<a<1
y

图 象

y
O

x

O

x

性 质

定义域:(0, +∞); 值域:R 过点(1, 0),即当x=1时,y=0.

2. 对数函数的性质:
a>1 0<a<1
y

图 象

y
O

x

O

x

性 x∈(0, 1)时,y<0; 质 x∈(1, +∞)时,y>0.

定义域:(0, +∞); 值域:R 过点(1, 0),即当x=1时,y=0.

2. 对数函数的性质:
a>1 0<a<1
y

图 象

y
O

x

O

x

性 x∈(0, 1)时,y<0; x∈(0, 1)时,y>0 质 x∈(1, +∞)时,y>0. x∈(1, +∞)时,y<0.

定义域:(0, +∞); 值域:R 过点(1, 0),即当x=1时,y=0.

2. 对数函数的性质:
a>1 0<a<1
y

图 象

y
O

x

O

x

性 x∈(0, 1)时,y<0; x∈(0, 1)时,y>0 质 x∈(1, +∞)时,y>0. x∈(1, +∞)时,y<0.
在(0,+∞)上是增函数

定义域:(0, +∞); 值域:R 过点(1, 0),即当x=1时,y=0.

2. 对数函数的性质:
a>1 0<a<1
y

图 象

y
O

x

O

x

性 x∈(0, 1)时,y<0; x∈(0, 1)时,y>0 质 x∈(1, +∞)时,y>0. x∈(1, +∞)时,y<0.
在(0,+∞)上是增函数

定义域:(0, +∞); 值域:R 过点(1, 0),即当x=1时,y=0.

在(0,+∞)上是减函数

练习 . 函数y=x+a与y=logax的图象可能是
y ① 1 O y 1 ③ O 1 x 1 x y (③)

1
② O y 1 ④ O 1 x

1

x

讲授新课
例1 比较下列各组数中两个值的大小:

(1) log 6 7, log 7 6

( 2) log 3 ? , log 2 0.8 ( 3) 6 , 0.7 , log 0.7 6
0.7 6

讲授新课
例1 比较下列各组数中两个值的大小:

(1) log 6 7, log 7 6

( 2) log 3 ? , log 2 0.8 ( 3) 6 , 0.7 , log 0.7 6
小结:当不能直接比较大小时,经常 在两个对数中间插入中间变量1或0等, 间接比较两个对数的大小.
0.7 6

练习 比较大小

(1) log 0.3 0.7, log 0.4 0.3
?1? ( 2) log 3.4 0.7, log 0.6 0.8, ? ? ? 3?
1 ? 2

(3) log 0.3 0.1, log 0.2 0.1

练习 比较大小

(1) log 0.3 0.7, log 0.4 0.3 log 0.3 0.7 ? log 0.4 0.3
?1? ( 2) log 3.4 0.7, log 0.6 0.8, ? ? ? 3?
1 ? 2

(3) log 0.3 0.1, log 0.2 0.1

练习 比较大小

(1) log 0.3 0.7, log 0.4 0.3 log 0.3 0.7 ? log 0.4 0.3
?1? ( 2) log 3.4 0.7, log 0.6 0.8, ? ? ? 3? 1 ? ?1? 2 log 3.4 0.7 ? log 0.6 0.8 ? ? ? ? 3?
1 ? 2

(3) log 0.3 0.1, log 0.2 0.1

练习 比较大小

(1) log 0.3 0.7, log 0.4 0.3 log 0.3 0.7 ? log 0.4 0.3
?1? ( 2) log 3.4 0.7, log 0.6 0.8, ? ? ? 3? 1 ? ?1? 2 log 3.4 0.7 ? log 0.6 0.8 ? ? ? ? 3?
1 ? 2

(3) log 0.3 0.1, log 0.2 0.1 log 0.3 0.1 ? log 0.2 0.1

P72例9 溶液酸碱度的测量. 溶液酸碱度是通过pH刻画的. pH的 计算公式为pH=-lg[H+],其中[H+]表 示溶液中氢离子的浓度,单位是摩尔/升. (1)根据对数函数性质及上述pH的计 算公式,说明溶液酸碱度与溶液中氢离 子的浓度之间的变化关系; (2)已知纯净水中氢离子的浓度为 [H+]=10-7摩尔/升,计算纯净水的pH.

课堂小结
1.比较对数大小的方法;

课堂小结
1.比较对数大小的方法; 2. 对数复合函数单调性的判断;

课堂小结
1. 复习巩固对数函数的性质及应用; 2.复习巩固比较对数大小; 3.对数函数的应用.

课后作业
1. 阅读教材P.70-P.72;


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