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Math Help - Why is 10^lg 5=5 and e^ln5=5, etc?

  1. #1
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    Why is 10^lg 5=5 and e^ln5=5, etc?

    Why is

    (10^\lg5)=5
    (e^\ln5)=5

    so on and so forth?
    Last edited by stupidguy; September 7th 2010 at 05:59 AM.
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  2. #2
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    Because the notation \log is being used to represent the logarithm of base 10, and \ln is being used to represent the logarithm of base e.
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    Quote Originally Posted by Prove It View Post
    Because the notation \log is being used to represent the logarithm of base 10, and \ln is being used to represent the logarithm of base e.
    Can you break it down further so that I can digest that information?
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    Thread closed. I dunno why i have double thread. Moderator can delete for me and transfer this reply over to the other?
    Last edited by stupidguy; September 7th 2010 at 06:15 AM.
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  5. #5
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    You should know that exponentials undo logarithms and vice versa.

    So a^{\log_a{x}} = x and \log_a{(a^x)} = x.


    In your first case, you're using \lg to represent \log_{10} and \ln to represent \log_e.
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  6. #6
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    Quote Originally Posted by stupidguy View Post
    Thread closed. I dunno why i have double thread. Moderator can delete for me and transfer this reply over to the other?
    Duplicate thread: http://www.mathhelpforum.com/math-he...tc-155461.html

    Thread closed.
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