chapter 8: logarithmic functions · pdf file08.06.2015 · 8.1 understanding...
TRANSCRIPT
![Page 1: Chapter 8: Logarithmic Functions · PDF file08.06.2015 · 8.1 Understanding Logarithms.notebook 4 3. Complete the following table: Function Domain Range xintercepts yintercept](https://reader030.vdocuments.mx/reader030/viewer/2022021501/5a9e11937f8b9ada718d4bc5/html5/thumbnails/1.jpg)
8.1 Understanding Logarithms.notebook
1
Chapter 8: Logarithmic Functions
![Page 2: Chapter 8: Logarithmic Functions · PDF file08.06.2015 · 8.1 Understanding Logarithms.notebook 4 3. Complete the following table: Function Domain Range xintercepts yintercept](https://reader030.vdocuments.mx/reader030/viewer/2022021501/5a9e11937f8b9ada718d4bc5/html5/thumbnails/2.jpg)
8.1 Understanding Logarithms.notebook
2
Chapter 8
8.1 Understanding LogarithmsPages 372 382
Investigating Logarithmic Functions:1. Complete the following table using and sketch on the axis provided.
x y
2
1
0
1
2
![Page 3: Chapter 8: Logarithmic Functions · PDF file08.06.2015 · 8.1 Understanding Logarithms.notebook 4 3. Complete the following table: Function Domain Range xintercepts yintercept](https://reader030.vdocuments.mx/reader030/viewer/2022021501/5a9e11937f8b9ada718d4bc5/html5/thumbnails/3.jpg)
8.1 Understanding Logarithms.notebook
3
2. Complete the table for the inverse of and sketch on the previous axis.
x y
![Page 4: Chapter 8: Logarithmic Functions · PDF file08.06.2015 · 8.1 Understanding Logarithms.notebook 4 3. Complete the following table: Function Domain Range xintercepts yintercept](https://reader030.vdocuments.mx/reader030/viewer/2022021501/5a9e11937f8b9ada718d4bc5/html5/thumbnails/4.jpg)
8.1 Understanding Logarithms.notebook
4
3. Complete the following table:
Function Domain Range xintercepts yintercept Asymptote
Inverse
4. Write the equation for the inverse in terms of y.
![Page 5: Chapter 8: Logarithmic Functions · PDF file08.06.2015 · 8.1 Understanding Logarithms.notebook 4 3. Complete the following table: Function Domain Range xintercepts yintercept](https://reader030.vdocuments.mx/reader030/viewer/2022021501/5a9e11937f8b9ada718d4bc5/html5/thumbnails/5.jpg)
8.1 Understanding Logarithms.notebook
5
Exponential Function:
Logarithmic Function: NOTE: Logarithms are exponents.
Inverse in exponential form:
** The exponent, y, to which c must be raised to equal x.
![Page 6: Chapter 8: Logarithmic Functions · PDF file08.06.2015 · 8.1 Understanding Logarithms.notebook 4 3. Complete the following table: Function Domain Range xintercepts yintercept](https://reader030.vdocuments.mx/reader030/viewer/2022021501/5a9e11937f8b9ada718d4bc5/html5/thumbnails/6.jpg)
8.1 Understanding Logarithms.notebook
6
Natural logarithm a logarithm with base e. ln is used instead of log.
Example:
logarithmic function a function of the form where c > 0 and
common logarithm a logarithm with base 10. usually not written. calculators only work in base 10.
Example:
![Page 7: Chapter 8: Logarithmic Functions · PDF file08.06.2015 · 8.1 Understanding Logarithms.notebook 4 3. Complete the following table: Function Domain Range xintercepts yintercept](https://reader030.vdocuments.mx/reader030/viewer/2022021501/5a9e11937f8b9ada718d4bc5/html5/thumbnails/7.jpg)
8.1 Understanding Logarithms.notebook
7
Examples:1. Rewrite the following logarithms in exponential form:
a) log216 = y b) log264 = y c) log10100 = y
d) log381 = y e) log2n = 5 f) logb49 = 2
![Page 8: Chapter 8: Logarithmic Functions · PDF file08.06.2015 · 8.1 Understanding Logarithms.notebook 4 3. Complete the following table: Function Domain Range xintercepts yintercept](https://reader030.vdocuments.mx/reader030/viewer/2022021501/5a9e11937f8b9ada718d4bc5/html5/thumbnails/8.jpg)
8.1 Understanding Logarithms.notebook
8
2. Express in logarithmic form:
a) 62 = 36 c) 4x = n
d) 35 = 243
![Page 9: Chapter 8: Logarithmic Functions · PDF file08.06.2015 · 8.1 Understanding Logarithms.notebook 4 3. Complete the following table: Function Domain Range xintercepts yintercept](https://reader030.vdocuments.mx/reader030/viewer/2022021501/5a9e11937f8b9ada718d4bc5/html5/thumbnails/9.jpg)
8.1 Understanding Logarithms.notebook
9
Example 1Page 374
Evaluating a LogarithmEvaluate the following:
![Page 10: Chapter 8: Logarithmic Functions · PDF file08.06.2015 · 8.1 Understanding Logarithms.notebook 4 3. Complete the following table: Function Domain Range xintercepts yintercept](https://reader030.vdocuments.mx/reader030/viewer/2022021501/5a9e11937f8b9ada718d4bc5/html5/thumbnails/10.jpg)
8.1 Understanding Logarithms.notebook
10
Example 1: Your TurnPage 374
Evaluate:
Answer
![Page 11: Chapter 8: Logarithmic Functions · PDF file08.06.2015 · 8.1 Understanding Logarithms.notebook 4 3. Complete the following table: Function Domain Range xintercepts yintercept](https://reader030.vdocuments.mx/reader030/viewer/2022021501/5a9e11937f8b9ada718d4bc5/html5/thumbnails/11.jpg)
8.1 Understanding Logarithms.notebook
11
Helpful Properties of logarithms:
since logarithms and exponents are inverse mathematical operations, they undo each other
![Page 12: Chapter 8: Logarithmic Functions · PDF file08.06.2015 · 8.1 Understanding Logarithms.notebook 4 3. Complete the following table: Function Domain Range xintercepts yintercept](https://reader030.vdocuments.mx/reader030/viewer/2022021501/5a9e11937f8b9ada718d4bc5/html5/thumbnails/12.jpg)
8.1 Understanding Logarithms.notebook
12
Example 2Page 375 Determining an unknown expression in logarithmic form:
Determine the value of x:
![Page 13: Chapter 8: Logarithmic Functions · PDF file08.06.2015 · 8.1 Understanding Logarithms.notebook 4 3. Complete the following table: Function Domain Range xintercepts yintercept](https://reader030.vdocuments.mx/reader030/viewer/2022021501/5a9e11937f8b9ada718d4bc5/html5/thumbnails/13.jpg)
8.1 Understanding Logarithms.notebook
13
Example 2: Your TurnPage 375
Determine the value of x:
Answer