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anonymous
 one year ago
I need help to simplify this equation
anonymous
 one year ago
I need help to simplify this equation

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\ln (\frac{ 1 }{ \sqrt{x} })  \ln (x) + \ln (x^3)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0first 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
 one year ago
Best ResponseYou've already chosen the best response.0\[\ln (1) = 0\] so we have, \[1/2\ln(x)  \ln(x)3\ln(x)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what is the next step

mathslover
 one year ago
Best ResponseYou've already chosen the best response.1Simply take \(\ln(x)\) common ..

mathslover
 one year ago
Best ResponseYou've already chosen the best response.1For 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
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 3lnx }{ 2 }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0nice trick to substitute, much easier to see!

mathslover
 one year ago
Best ResponseYou've already chosen the best response.1Uhm... 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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