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Math Help - Logarithm issues.

  1. #1
    Member MathBlaster47's Avatar
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    Logarithm issues.

    I have a question that asks me to find the value of the expression (.65)^5 in logarithmic form.

    Am I correct in assuming that I should be looking the logarithm that is five times greater than that of .65?

    Or is the answer:
    \log (.68)^5=5\log(.68)=5\log (6.8*10^-1)Therefore the answer is 5*.8129 or 4.0645+(-1)=3.0645 ?
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by MathBlaster47 View Post
    I have a question that asks me to find the value of the expression (.65)^5 in logarithmic form.

    Am I correct in assuming that I should be looking the logarithm that is five times greater than that of .65? e^(i*pi) : Yep, due to the power law

    Or is the answer:
    \log (.68)^5=5\log(.68)=5\log (6.8*10^-1) e^(i*pi): Indeed

    Therefore the answer is 5*.8129 or 4.0645+(-1)=3.0645 ? e^(i*pi) : No, you've made a decimal approximation and the question doesn't ask for this
    \log (.68)^5=5\log(.68)=5\log (6.8 \cdot 10^{-1}) = 5\log (6.8) - 1
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  3. #3
    Member MathBlaster47's Avatar
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    Thanks for your help.
    I think I should have been a little more careful how I phrased my question, the question asks me to use a table of logarithms to derive my answer, I just wanted to do my due diligence and try to do the working myself.

    Follow up question: Is my decimal approximation satisfactory as an answer, given that I was asked to use a table?
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  4. #4
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    Quote Originally Posted by MathBlaster47 View Post
    Thanks for your help.
    I think I should have been a little more careful how I phrased my question, the question asks me to use a table of logarithms to derive my answer, I just wanted to do my due diligence and try to do the working myself.

    Follow up question: Is my decimal approximation satisfactory as an answer, given that I was asked to use a table?
    Hi Mathblaster47,

    you made one error, apart from writing 0.68 instead of 0.65 ...

    5[log(6.5X10^{-1})]=5[log(6.5)+log\left(10^{-1}\right)]=5[log(6.5)-1]=5log(6.5)+5(-1)
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  5. #5
    Member MathBlaster47's Avatar
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    Quote Originally Posted by Archie Meade View Post
    Hi Mathblaster47,

    you made one error, apart from writing 0.68 instead of 0.65 ...

    5[log(6.5X10^{-1})]=5[log(6.5)+log\left(10^{-1}\right)]=5[log(6.5)-1]=5log(6.5)+5(-1)
    Hmmm....gotta stop typing so fast....Silly typos!

    Ok, so the final answer is 5(.8129)+5(-1)=4.0645+(-5)?
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  6. #6
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    Yes Mathblaster47,

    the answer is negative,
    so check that

    (0.65)^5=10^{answer}

    or

    5log(0.65)=(answer)[log(10)]
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