4.5 Apply Properties of Logarithms

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4.5 Apply Properties of Logarithms. p. 259 What are the three properties of logs? How do you expand a log? Why? How do you condense a log?. Properties of Logarithms. Use log 5 3 ≈.683 and log 5 7≈1.209. log 5 21 = log 5 (3 ·7)= log 5 3 + log 5 7≈ .683 + 1.209 = 1.892. - PowerPoint PPT Presentation

Transcript of 4.5 Apply Properties of Logarithms

  • 4.5 Apply Properties of Logarithmsp. 259

    What are the three properties of logs?How do you expand a log? Why?How do you condense a log?

  • Properties of Logarithms

  • Use log53.683 and log571.209log521 =log5(37)=log53 + log57.683 + 1.209 =1.892

  • Use log53.683 and log571.209Approximate:log549 =log572 =2 log57 2(1.209)=2.418

  • Write 40 as 8 5.Product propertySimplify.

  • Expanding LogarithmsYou can use the properties to expand logarithms.

    log2 =

    log27x3 - log2y = log27 + log2x3 log2y =log27 + 3log2x log2y

  • Your turn!Expand:log 5mn =log 5 + log m + log n

    Expand:log58x3 =log58 + 3log5x

  • Condensing Logarithmslog 6 + 2 log2 log 3 =log 6 + log 22 log 3 =log (622) log 3 =

    log =

    log 8

  • SOLUTIONEvaluate using common logarithms and natural logarithms.Using common logarithms:Using natural logarithms:

  • What are the three properties of logs?Productexpanded add each, Quotientexpand subtract, Powerexpanded goes in front of log.How do you expand a log? Why?Use logb before each addition or subtraction change. Power property will bring down exponents so you can solve for variables.How do you condense a log?Change any addition to multiplication, subtraction to division and multiplication to power. Use one logb

  • For a sound with intensity I (in watts per square meter), the loudness L(I) of the sound (in decibels) is given by the function

  • Product propertySimplify.SOLUTIONLet I be the original intensity, so that 2I is the doubled intensity.Increase in loudnessWrite an expression.Substitute.Distributive propertyUse a calculator.

  • 4.5 Assignmentpage 262, 7-41 odd

  • Properties of Logarithms Day 2What is the change of base formula?What is its purpose?

  • Your turn!Condense:log57 + 3log5t =log57t3

    Condense:3log2x (log24 + log2y)=

    log2

  • Change of base formula:a, b, and c are positive numbers with b1 and c1. Then:

    logca =

    logca = (base 10)

    logca = (base e)

  • Examples:Use the change of base to evaluate:log37 =(base 10)log 7 log 31.771(base e)ln 7 ln 31.771

  • Use the change-of-base formula to evaluate the logarithm.SOLUTIONSOLUTION

  • What is the change of base formula?

    What is its purpose?Lets you change on base other than 10 or e to common or natural log.

  • 4.5 Assignment Day 2Page 262, 16- 42 even, 45-59 odd