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Math Help - Using properties of logarithms to compute

  1. #1
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    Using properties of logarithms to compute

    Given ln 2 = 0.6931 and ln 3 = 1.0986, use properties of logarithms to compute:

    ln square root(8/27), Sorry I have no idea how to put a square root sign in.


    Thank you very much
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Using properties of logarithms to compute

    Can you write the argument for the log function as a fraction involving only 2 and 3 raised to some power?
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  3. #3
    Junior Member ReneG's Avatar
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    Re: Using properties of logarithms to compute

    \ln{\sqrt{\frac{8}{27}}} Given
    = \ln{\left\frac{8}{27}\right} ^\frac{1}{2} Equivalent fractional exponent
    =\frac{\ln{\frac{8}{27}}}{2} Log property: \log_b{a^n} = n\log_b{a}
    =\frac{\ln{8} - \ln{27}}{2} Log property: \log_b{\frac{a}{n}} = \log_b{a} - \log_b{n}
    =\frac{\ln{2^3} - \ln{3^3}}{2} 8 = 2^3 and 27 = 3^3
    =\frac{3\ln{2} - 3\ln{3}}{2} Log property: \log_b{a^n} = n\log_b{a}
    =\frac{3(0.6931) - 3(1.0986)}{2} Substitute \ln 2 and \ln 3
    \approx -0.60825 Simplify with calculator
    Last edited by ReneG; May 27th 2013 at 02:10 AM.
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