Properties of Logarithmic Functions Objective: Simplify and evaluate expressions involving...

Upload
aidenfitzpatrick 
Category
Documents

view
220 
download
1
Embed Size (px)
Transcript of Properties of Logarithmic Functions Objective: Simplify and evaluate expressions involving...
Properties of Logarithmic Functions
Objective: Simplify and evaluate expressions involving logarithms.
7z 12t 3c
7z 12t 3c
3
3
nm
66ba 48sr
Product and Quotient Properties of Logarithms
• For
• Product Property
:1,0,0,0 bbnm
nmmn bbb loglog)(log
Product and Quotient Properties of Logarithms
• For
• Product Property
• Quotient Property
:1,0,0,0 bbnm
nmmn bbb loglog)(log
nm bbnm
b logloglog
Product and Quotient Properties of Logarithms
• For
• Product Property
• Quotient Property
• You can use these properties to evaluate logarithmic expressions.
:1,0,0,0 bbnm
nmmn bbb loglog)(log
nm bbnm
b logloglog
Example 1
Example 1
Example 1
Try This
• Given that , approximate each expression.
585.13log2
18log2 43
2log
Try This
• Given that , approximate each expression.
585.13log2
18log2 43
2log
170.4585.1585.11
3log3log2log
332log
222
2
Try This
• Given that , approximate each expression.
585.13log2
18log2 43
2log
170.4585.1585.11
3log3log2log
332log
222
2
415.2585.1
4log3log 22
Example 2
Example 2
Example 2
Try This
• Write each expression as a single logarithm. Then, simplify if possible.
6log18log 44 yyx bb log3log4log 3
Try This
• Write each expression as a single logarithm. Then, simplify if possible.
6log18log 44 yyx bb log3log4log 3
3loglog 4618
4
Try This
• Write each expression as a single logarithm. Then, simplify if possible.
6log18log 44 yyx bbb log3log4log
3loglog 4618
4 34
34 loglog x
byyx
b
The Power Property of Logarithms
• For , and any real number p:1,0,0,0 bbnm
mpm bp
b loglog
Example 3
Example 3
Try This
• Evaluate .1003 27log
Try This
• Evaluate .1003 27log
300310027log10027log 3100
3
ExponentialLogarithmic Inverse Properties
• For b > 0 and : 1b
0for log xxb xb
0for log xxb xb
Example 4
Example 4
Example 4
Try This
• Evaluate each expression.
81log7 311log7 8log5
8338log
Try This
• Evaluate each expression.
81log7 311log7 8log5
8338log
7411
Try This
• Evaluate each expression.
81log7 311log7 8log5
8338log
7411 1385
OnetoOne Property of Logarithms
• If , then x = y.yx bb loglog
Example 5
Example 5
Example 5
Homework
• Page 382• 1361 odd