anonymous
  • anonymous
I need help to simplify this equation
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
\[\ln (\frac{ 1 }{ \sqrt{x} }) - \ln (x) + \ln (x^3)\]
anonymous
  • anonymous
first step is this: \[\ln (1) - \ln (x ^{1/2}) - \ln (x) + \ln (x^3)\] secod step is this \[\ln (1) - 1/2\ln (x) - \ln(x) + 3\ln(x)\]
anonymous
  • anonymous
\[\ln (1) = 0\] so we have, \[-1/2\ln(x) - \ln(x)-3\ln(x)\]

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anonymous
  • anonymous
what is the next step
mathslover
  • mathslover
Simply take \(\ln(x)\) common ..
mathslover
  • mathslover
For a second, let us imagine \(\ln(x)\) as any variable \(t\) So, we have: \(-\cfrac{1}{2}t -t - 3t\) Now, you know how to simplify this, don't you? After simplifying, put \(t\) back as \(\ln(x)\)
anonymous
  • anonymous
\[\frac{ 3lnx }{ 2 }\]
anonymous
  • anonymous
nice trick to substitute, much easier to see!
anonymous
  • anonymous
thanks alot!
mathslover
  • mathslover
Uhm... I guess, you need to check your arithmetic again. We have : \(\cfrac{-1}{2} t - t - 3t = -t\left( \cfrac{1}{2} + 1 + 3 \right) = -t \left( \cfrac{9}{2} \right) = \cfrac{-9t}{2} \) Or : \(-\cfrac{9}{2} \ln x \) And you're welcome. :)

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