Properties of Logarithms

//Properties of Logarithms
Properties of Logarithms 2017-11-13T22:01:53+00:00

    As you have probably noticed, your calculator only has two log buttons: the common log, log 10 and the natural log, log e or ln. Fortunately, by using the change of base theorem, you can evaluate a log of any base.

    Change of Base Theorem

    Change of base

    Evaluate

    Round the result to three decimal places.

    log 6 9

    Take the log of 9 divided by the log of 6. The result is 1.226.

    log 2 14

    Divide the log of 14 by the log of 2 The answer is 3.807.

    log 1/4 12

    You can also use the natural log instead of the common log. Take ln 12 / ln .25. The result is -1.792.

    Evaluate

    Do not use a calculator.

    SimplifyLogs

    Properties of Logarithms

    PropertiesofLogs

    Because the answer to a logarithmic equation is the exponent in an exponential equation, it makes sense that logarithms should behave as exponents do.

    Expand

    log 5 3x2y

    ExpandLogarithm

    Condense

    3 ln(x – 5) + ln x

    condenselogarithm

    Precalculus with Limits – Larson & Hostetler p.239-245