Results 1 to 7 of 7

Thread: how to get from ln(4)/2 to ln2 ?

  1. #1
    Member
    Joined
    Jul 2009
    From
    London
    Posts
    109

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

    Hi

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

    So to solve I do this:

    $\displaystyle 2t = ln4$

    $\displaystyle t = ln4/2$

    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
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    6

    Re: how to get from ln(4)/2 to ln2 ?

    Quote Originally Posted by angypangy View Post
    Hi

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

    So to solve I do this:

    $\displaystyle 2t = ln4$

    $\displaystyle t = ln4/2$

    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 $\displaystyle \ln \sqrt{a}= \frac{\ln a}{2}$...



    Marry Christmas from Serbia

    $\displaystyle \chi$ $\displaystyle \sigma$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jul 2009
    From
    London
    Posts
    109

    Re: how to get from ln(4)/2 to ln2 ?

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



    Marry Christmas from Serbia

    $\displaystyle \chi$ $\displaystyle \sigma$
    Please explain.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,776
    Thanks
    3028

    Re: how to get from ln(4)/2 to ln2 ?

    $\displaystyle a \log(b)= \log(b^a)$
    Last edited by CaptainBlack; Dec 22nd 2011 at 12:20 AM. Reason: tidy LaTeX
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    6

    Re: how to get from ln(4)/2 to ln2 ?

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



    Marry Christmas from Serbia

    $\displaystyle \chi$ $\displaystyle \sigma$
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Jul 2009
    From
    London
    Posts
    109

    Re: how to get from ln(4)/2 to ln2 ?

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



    Marry Christmas from Serbia

    $\displaystyle \chi$ $\displaystyle \sigma$
    So it is like this?

    $\displaystyle \frac{\ln 4}{2}= \frac{1}{2} * ln4 = ln4^\frac{1}{2} = ln2$
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,216
    Thanks
    3702

    Re: how to get from ln(4)/2 to ln2 ?

    or ...

    $\displaystyle \frac{\ln{4}}{2} = \frac{\ln{2^2}}{2} = \frac{2\ln{2}}{2} = \ln{2}$
    Follow Math Help Forum on Facebook and Google+

Search tags for this page

Search Tags


/mathhelpforum @mathhelpforum