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Math Help - how to get from ln(4)/2 to ln2 ?

  1. #1
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    how to get from ln(4)/2 to ln2 ?

    Hi

    I have an equation e^{2t} = 4

    So to solve I do this:

    2t = ln4

    t = ln4/2

    That's fine, but answer is t = ln2. How do you get from ln2?

    I can see that ln(4)/2 is equivalent to ln2 - but what is algebra to get to ln2?

    Angus
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  2. #2
    MHF Contributor chisigma's Avatar
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    Re: how to get from ln(4)/2 to ln2 ?

    Quote Originally Posted by angypangy View Post
    Hi

    I have an equation e^{2t} = 4

    So to solve I do this:

    2t = ln4

    t = ln4/2

    That's fine, but answer is t = ln2. How do you get from ln2?

    I can see that ln(4)/2 is equivalent to ln2 - but what is algebra to get to ln2?

    Angus
    Apply the identity \ln \sqrt{a}= \frac{\ln a}{2}...



    Marry Christmas from Serbia

    \chi \sigma
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  3. #3
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    Re: how to get from ln(4)/2 to ln2 ?

    Quote Originally Posted by chisigma View Post
    Apply the identity \ln \sqrt{a}= \frac{\ln a}{2}...



    Marry Christmas from Serbia

    \chi \sigma
    Please explain.
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  4. #4
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    Re: how to get from ln(4)/2 to ln2 ?

    a \log(b)= \log(b^a)
    Last edited by CaptainBlack; December 22nd 2011 at 12:20 AM. Reason: tidy LaTeX
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  5. #5
    MHF Contributor chisigma's Avatar
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    Re: how to get from ln(4)/2 to ln2 ?

    Quote Originally Posted by angypangy View Post
    Please explain.
    \frac{\ln 4}{2}= \ln \sqrt{4}= \ln 2



    Marry Christmas from Serbia

    \chi \sigma
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  6. #6
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    Re: how to get from ln(4)/2 to ln2 ?

    Quote Originally Posted by chisigma View Post
    \frac{\ln 4}{2}= \ln \sqrt{4}= \ln 2



    Marry Christmas from Serbia

    \chi \sigma
    So it is like this?

    \frac{\ln 4}{2}= \frac{1}{2} * ln4 = ln4^\frac{1}{2} = ln2
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  7. #7
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    Re: how to get from ln(4)/2 to ln2 ?

    or ...

    \frac{\ln{4}}{2} = \frac{\ln{2^2}}{2} = \frac{2\ln{2}}{2} = \ln{2}
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