7-4 Properties of Logarithms
Algebra 2H
[For any positive numbers n,mandb(b1)]
1. Product Property of Logs: _
2. Quotient Property of Logs: _
3. Power Property of Logs: _
4. Logarithm of 1 Property: _
/
Alg 2 7.1 Worksheet name < E .
Complete each statement.
1. A function of the form f(x) = ab" is called an exponential function When b is
greater than 1.
2. A function of the form f(x) = ab" is
Sin
Write each exponential equation in log form:
9. 35:243 10. 510:1 11. x=343 o z
.. t 9 :2 :
'093245 5 legal] C) J .2 l
l
l
l
l
Write each log in exponential form:
12. logs4512 = 1.5 13. 1090
7-6 Natural Logs and Base e
Algebra 2H
natural logarithm
natural logarithmic function
x
F(x) = ex
-2
-1
0
1
2
x
F-1(x)=lnx
y
10
8
6
4
2
10 8
6
4
2
2
2
4
6
8
10
x
4
6
8
10
All the properties from 7-4 a
7-1 Exponential Functions and Logarithms
Algebra 2H
exponential function
base
asymptote
exponential growth
exponential decay
Ex 1: f(x) = 1.5x
y
12
10
x
y
8
6
4
2
Describe the graph:
12 10 8
6
4
2
2
2
7-5 Exponential and Logarithmic Equations
Algebra 2H
exponential equation
logarithmic equation
Two methods to solve exponential equations:
1. Write both sides with the same base.
2. Take the log of bo
Ex 4: Clara invests $5000 in an account that pays 6.25% interest per year. After
how many years will her investment be worth $10,000?
Ex 5: A city population, which was initially 15,500, has been drop
Answers: Chapter 7 Exponential and Logarithmic Functions
Study Guide: Review; P SS Li
4.
'aJZQg'Jozy
= 845
5;:
109'.)-
5
5'
Sludem population
§
0 tiléwédp
2 E 10 (4 m
Time(yr)
@ =
7-1 Exponential Functions and Logarithms
Algebra 2H
exponential function
base
asymptote
exponential growth
exponential decay
Ex 1: f(x) = 1.5x
y
12
10
x
y
8
6
4
2
Describe the graph:
12 10 8
6
4
2
2
2