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.
$\endgroup$ 53 Answers
$\begingroup$$a\ln(b) = \ln(b^a)$ and $\ln(a)+\ln(b)=\ln(ab)$ from this you can show $\ln(a)-\ln(b) = \ln(a)+\ln(b^{-1}) = \ln(\frac{a}{b})$ which should be all you need
$\endgroup$ 4 $\begingroup$Hint: $\ln a^b= b \ln a, \ln ab = \ln a + \ln b$
$\endgroup$ $\begingroup$$$3 \ln 2 - \frac{1}{2}\ln 4=3 \ln 2 - \ln 4^{\frac{1}{2}}=3 \ln 2- \ln 2=2 \ln 2$$
$\endgroup$
