Embed Size (px)
Citation preview
8.1 Understanding Logarithms.notebook
1
Chapter 8: Logarithmic Functions
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
8.1 Understanding Logarithms.notebook
3
2. Complete the table for the inverse of and sketch on the previous axis.
x y
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.
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.
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:
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
8.1 Understanding Logarithms.notebook
8
2. Express in logarithmic form:
a) 62 = 36 c) 4x = n
d) 35 = 243
8.1 Understanding Logarithms.notebook
9
Example 1Page 374
Evaluating a LogarithmEvaluate the following:
8.1 Understanding Logarithms.notebook
10
Example 1: Your TurnPage 374
Evaluate:
Answer
8.1 Understanding Logarithms.notebook
11
Helpful Properties of logarithms:
since logarithms and exponents are inverse mathematical operations, they undo each other
8.1 Understanding Logarithms.notebook
12
Example 2Page 375 Determining an unknown expression in logarithmic form:
Determine the value of x:
8.1 Understanding Logarithms.notebook
13
Example 2: Your TurnPage 375
Determine the value of x:
Answer
