Logarithms – An Introduction Check for Understanding – 3103.3.16 Prove basic properties of...

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Transcript of Logarithms – An Introduction Check for Understanding – 3103.3.16 Prove basic properties of...

  • Logarithms An IntroductionCheck for Understanding 3103.3.16

    Prove basic properties of logarithms using propertiesof exponents and applythose properties to solveproblems.

    Check for Understanding 3103.3.17

    Know that the logarithm andexponential functions areinverses and use this informationto solve real-world problems.

  • What are logarithms?logarithm : noun the exponent that indicates the power to which a base number is raised to produce a given number

    Merriam-Webster Online (June 2, 2009)

  • What are logarithms used for? pH Scale

    Richter Scale

    Decibels

    Radioactive Decay

    Population Growth

    Interest Rates

    Telecommunication

    Electronics

    Optics

    Astronomy

    Computer Science

    Acoustics

    And Many More!

  • My calculator has a log button why cant I just use that?The button on your calculator only worksfor certain types of logarithms; these are called common logarithms.

  • Try These On Your Calculatorlog245log101002PX1.65325.4919P

  • Whats the difference?The log button on the calculator is used to evaluate common logarithms, which have a base of 10.

    If a base is not written on a logarithm, the base is understood to be 10.

    log 100 is the same as log10100

  • The logarithmic function is an inverse of the exponential function.

  • Logarithm with base bThe basic mathematical definition of logarithms with base b is

    logb x = y iff by = x

    b > 0, b 1, x > 0

  • Write each equation in exponential form.log6 36 = 2

    6

    2=362. log125 5 = 1 5

    =5125

  • Write each equation in logarithmic form.3. 23 = 8

    2=37-2 = 1 49

    log

    =2log87

  • Evaluate each expression5. log4 64= x6. log5 625 = x4x= 645x= 6254x= 43x = 35x= 54x = 4

  • Evaluate each expressionlog2 128

    8. log3 9. log8 4

    10. log11 1

  • Evaluate each expressionlog2 128

    7

    log3

    4 9. log8 4

    log11 1

    0

  • Solve each equation11. log4 x = 3log4 x = 3 2 43= x64 = xx = 84= x

  • Evaluate each expression13. log6 (2y + 8) = 2

    14. logb 16 = 4 15. log7 (5x + 7) = log7 (3x + 11)

    16. log3 (2x 8) = log3 (6x + 24)

  • Evaluate each expression13. log6 (2y + 8) = 2

    14

    logb 16 = 4

    2 15. log7 (5x + 7) = log7 (3x + 11)

    2

    16. log3 (2x 8) = log3 (6x + 24)