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: _
[For a>0 and a1 and any base b such that b>0 and b1]
C
/
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 called an exponential D / \ function when b is a
numbe
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. 1090125 = -3 14. Iogqx = 70 15. Ing12 = 3
(cat's5)"; 23:17
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 also apply to natural logarithms.
Ex. 1 Simplify.
lne-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 both sides.
Ex 1: Solve for the variable.
98-x = 27x-3
5x
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 dropping by 3% a
year. Write an exponential function and gr