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Math Help - Use Logarithms to evaluate the expression

  1. #1
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    Use Logarithms to evaluate the expression

    Use logarithms to evaluate the given expression

    (7.32^(1/10))*(2470^(30))

    The books answer is 7.37 * 10^(101)

    I'm not exactly sure how to go about doing this problem.
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  2. #2
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    Quote Originally Posted by OzzMan View Post
    Use logarithms to evaluate the given expression

    (7.32^(1/10))*(2470^(30))

    The books answer is 7.37 * 10^(101)

    I'm not exactly sure how to go about doing this problem.
    Let N = 7.32^{1/10} \cdot 2470^{30}

    Then
    log(N) = log(7.32^{1/10} \cdot 2470^{30})
    (I'm using log to the base 10 but feel free to use any base you desire.)

    log(N) = log(7.32^{1/10}) + log(2470^{30})

    log(N) = \frac{1}{10}~log(7.32) + 30~log(2470)

    Now grab a calculator:
    log(N) = 101.867

    Now split the integer from the decimal part:
    log(N) = 101 + 0.867

    And raise both sides to the power of 10:
    10^{log(N)} = 10^{101 + 0.867}

    N = 10^{0.867} \cdot 10^{101}

    And use your calculator on that first factor:
    N = 7.36817 \times 10^{101}

    Of course you might (as I do) own a calculator that you can multiply the original form out directly.

    -Dan
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  3. #3
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    Thanks. Makes sense now. My calculator gets overflow when i multiply it directly out though.
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