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Homework Help: Question of natural log.

  1. May 18, 2013 #1
    I want to verify this:

    [tex]2ln(x)-ln(2x)=ln(x^2)-ln(2x)=ln\left(\frac{x^2}{2x}\right)=ln\left(\frac x 2\right)[/tex]
    [tex]ln(2x)-ln(x)=\ln\left(\frac {2x}{x}\right)=ln(2)[/tex]

  2. jcsd
  3. May 18, 2013 #2
    They're pretty straight applications of the log laws

    [itex]log_{c}(a^{b}) = blog_{c}(a)[/itex]

    [itex]log_{c}(a) - log_{c}(b) = log_{c}(\frac{a}{b})[/itex]
  4. May 18, 2013 #3


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    You can also do the first one as

    ##\displaystyle 2\ln(x)-\ln(2x)=2\ln(x)-(\ln(x)+\ln(2))=\ln(x)-\ln(2)=\ln(x/2)
  5. May 18, 2013 #4
    Thanks, I am so rusty on these math as I don't use it often!!! I was stuck for a day in the other thread about sine and cosine integrals because of this. All of a sudden, I remember all the log things and it answer my question there.

    Many thanks.
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