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How would you go about simplifying this equation: $$3 \ln 2 - \frac{1}{2}\ln 4$$ I am not very familiar with logarithms and how they work, the process is still confusing me.

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    So let us start with 3 ln 2. This is ln x for some x. Can you see what is x?2012-10-30
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    Please do not write 1/2 ln 4. Some people will read this as 1/(2 ln 4). You could write (1/2) ln 4, (ln 4)/2, or, preferably, $\frac {\ln 4}2$2012-10-30
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    Noted, thanks for the tip.2012-10-30
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    @Adi Dani: we avoid using double dollar signs in the title. It takes lots of room. In the body is fine.2012-10-30
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    o.k @Ross millikan2012-10-30

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$a\ln(b) = \ln(b^a)$ and $\ln(a)+\ln(b)=\ln(ab)$ from this you can show $\ln(a)-\ln(b) = \ln(a)+\ln(b^{-1}) = \ln(\frac{a}{b})$ which should be all you need

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    Thank you, the rules that you gave were helpful!2012-10-30
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    @Craig No problem, let me know what you're thinking and I'll talk you through it in the comments if you want.2012-10-30
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    I think I understand how it works now. Simplified, it should be this: ln(4)... Correct?2012-10-30
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    Yep, you've got it. @Craig2012-10-30
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Hint: $\ln a^b= b \ln a, \ln ab = \ln a + \ln b$

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$$3 \ln 2 - \frac{1}{2}\ln 4=3 \ln 2 - \ln 4^{\frac{1}{2}}=3 \ln 2- \ln 2=2 \ln 2$$