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Math Help - logs

  1. #1
    Member princess_anna57's Avatar
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    Talking logs

    How do I solve the following without using my calculator:

    a) e^In 1000
    b) log10(100e)
    c) In e
    d) log10 (e^8)
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by princess_anna57 View Post
    How do I solve the following without using my calculator:

    a) e^In 1000
    b) log10(100e)
    c) In e
    d) log10 (e^8)
    hints:

    for a>0, b>0, d>0 and any c \in \mathbb{R}
    e^{\ln a}=a
    \log_a a = 1
    log_a b^c = c \log_a b
    \log_a (bd) =  \log_a b + \log_a d
    \log_a \left(\frac{b}{d}\right) =  \log_a b - \log_a d
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  3. #3
    Member princess_anna57's Avatar
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    :)

    So for a) the answer is 1,000?
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  4. #4
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by princess_anna57 View Post
    So for a) the answer is 1,000?
    right!
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  5. #5
    Member princess_anna57's Avatar
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    =)

    and d) is 8 log 10e?

    I still don't know how to do b) or c).
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  6. #6
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by princess_anna57 View Post
    and d) is 8 log 10e?

    I still don't know how to do b) or c).
    assuming you meant 8 \log_{10} e, then you are right..

    for b) \log_{10} (100e) = \log_{10} 100 + \log_{10} e = \log_{10} 10^2 + \log_{10} e = ...

    for c) take note that \ln a = \log_e a.. (a>0)
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