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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0So 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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0Please 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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0Noted, thanks for the tip. – 2012-10-30
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0@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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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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0Thank you, the rules that you gave were helpful! – 2012-10-30
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0@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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1I think I understand how it works now. Simplified, it should be this: ln(4)... Correct? – 2012-10-30
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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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$$3 \ln 2 - \frac{1}{2}\ln 4=3 \ln 2 - \ln 4^{\frac{1}{2}}=3 \ln 2- \ln 2=2 \ln 2$$