Section 5.4 class notes_0

# Section 5.4 class notes_0 - Objective 3 Solving Logarithmic...

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Section 5.4 Properties of Logarithms Objective 1: Using the Product Rule, Quotient Rule and Power Rule for Logarithms Properties of Logarithms If 0, 1 b b , u and v represent positive numbers, and r is any real number, then log log log b b b uv u v = + Product Rule for Logarithms log log log b b b u u v v = - Quotient Rule for Logarithms log log b b r u r u = Power Rule for Logarithms Warning! ( 29 log is NOT equiva lent to log log b b b u v u v + + . ( 29 log is NOT equivalent to log log b b b u v u v - - . log is NOT equivalent to log log log b b b b u u v v - . ( 29 log is NOT equivalent to log b b r u r u . 5.4.4, 5, 7, or 9 Use the properties of logarithms to expand the expression. Wherever possible, evaluate the expression. Objective 2: Expanding and Condensing Logarithmic Expressions 5.4.13 Use the properties of logarithms to expand the expression. Wherever possible, evaluate the expression.

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5.4.27 Use the properties of logarithms to rewrite the expression as a single logarithm. Wherever possible, evaluate the expression.
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Unformatted text preview: Objective 3: Solving Logarithmic Equations Using the Logarithm Property of Equality The Logarithm Property of Equality If a logarithmic equation can be written in the form log log b b u v = , then u v = . Furthermore, if u v = , then log log b b u v = . 5.4.34 Use the properties of logarithms and the logarithm property of equality to solve the equation. Objective 4: Using the Change of Base Formula Change of Base Formula For any positive base 1 b ≠ and for any positive real number u , then log log log a b a u u b = where a is any positive number such that 1 a ≠ . 5.4.40 Use the change of base formula and a calculator to approximate the following expressions. Do not round until the final answer. Then round to four decimal places as needed. 5.4.47 Solve the equation and simplify the answer....
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Section 5.4 class notes_0 - Objective 3 Solving Logarithmic...

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