Download 171S5.4_p Properties of Logarithms

171S5.4_p Properties of Logarithms
MAT 171 Precalculus Algebra
Trigsted ­ Pilot Test
Dr. Claude Moore ­ Cape Fear Community College
CHAPTER 5: Exponential and Logarithmic Functions and Equations
5.1 Exponential Functions
5.2 The Natural Exponential Function
5.3 Logarithmic Functions
5.4 Properties of Logarithms
5.5 Exponential and Logarithmic Equations 5.6 Applications of Exponential and Logarithmic Functions
Properties of Logarithms
April 14, 2011
Objectives
1. Using the Product Rule, Quotient Rule and
Power Rule for Logarithms
2. Expanding and Condensing Logarithmic
Expressions
3. Solving Logarithmic Equations Using the
Logarithm Property of Equality
4. Using the Change of Base Formula
Use the product rule for logarithms to expand each expression. Assume x > 0.
If b > 0, b ≠ 1, u and v represent positive numbers, and r is any real number, then
Product rule: Quotient rule: Use the quotient rule for logarithms to expand each expression. Assume x > 0.
Power rule: 1
171S5.4_p Properties of Logarithms
Use the power rule for logarithms to expand each expression. Assume x > 0.
Use the properties for logarithms to condense each expression. Assume x > 0.
April 14, 2011
Use the properties for logarithms to expand each expression. Assume x > 0.
Logarithm Property of Equality
If a logarithmic equation can be written in the form then u = v.
Furthermore, if u = v, then Domain of log x is x > 0
x = -8 is an extraneous solution
Solution is x = 8
2
171S5.4_p Properties of Logarithms
Change of Base Formula
April 14, 2011
Use the Change of Base Formula to solve.
For any positive base b ≠ 1 and for any positive real number u, then where a is any positive number such that a ≠ 1. 3
171S5.4_p Properties of Logarithms
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171S5.4_p Properties of Logarithms
April 14, 2011
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