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.
Simplify: $3 \ln 2 - \frac{1}{2}\ln 4$
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$\begingroup$
calculus
logarithms
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0o.k @Ross millikan – 2012-10-30
3 Answers
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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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0Yep, you've got it. @Craig – 2012-10-30
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Hint: $\ln a^b= b \ln a, \ln ab = \ln a + \ln b$
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$3 \ln 2 - \frac{1}{2}\ln 4=3 \ln 2 - \ln 4^{\frac{1}{2}}=3 \ln 2- \ln 2=2 \ln 2$