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8.5 Properties of Logarithms 3/21/2014

8.5 Properties of Logarithms 3/21/2014. Properties of Logarithms. Let m and n be positive numbers and b ≠ 1, Product Property Quotient Property Power Property. Expand and Condense Logarithmic Expressions. Expand : is a sum and/or difference of logs. Condense: A single log expression.

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8.5 Properties of Logarithms 3/21/2014

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  1. 8.5 Properties of Logarithms3/21/2014

  2. Properties of Logarithms Let m and n be positive numbers and b ≠ 1, Product Property Quotient Property Power Property

  3. Expand and Condense Logarithmic Expressions Expand: is a sum and/or difference of logs. Condense: A single log expression.

  4. Example 2 3x 3x a. b. b. log4 5x2 log7 log7 y y SOLUTION a. log4 5x2 log45 log4x2 Product property + = Power property log452 log4x + = log73x log7y – Quotient property = Expand a Logarithmic Expression Expand the expression. Assume all variables are positive. log73 log7xlog7y – Product property + =

  5. Expand and Condense Logarithmic Expressions Checkpoint 5. log2 5x log2 x ANSWER log2 5 + 5x 6. log 2x 3 3 log x ANSWER log 2 + log3 7 7. ANSWER 8. log6 4 2 log6x log6y ANSWER 4x2 – + log6 y log3 5 log3x log3 7 – + Expand the expression. Assume all variables are positive.

  6. Example 3 a. log 16 2 log 2 – SOLUTION a. log 16 2 log 2 log 16 log 22 – – Power property = Quotient property = Simplify. log 4 = 16 log 22 Condense a Logarithmic Expression Condense the expression.

  7. Example 3 3 log 5 log 4 log 53 log 4 Power property + + = Product property log ( ) 53 4 • = b. 3 log 5 log 4 + Simplify. log 500 = Condense a Logarithmic Expression SOLUTION

  8. Expand and Condense Logarithmic Expressions Checkpoint x3 9. log5 12 log5 4 ANSWER – log5 3 y 10. log2 7 log2 5 ANSWER + log2 35 11. log 4 2log 3 log 36 ANSWER + 12. 3 log x log y log ANSWER – Condense the expression. Assume all variables are positive.

  9. Homework:8.5 p.445 #34-56even

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