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QUESTION
How do you prove that ##(1/2)(ln2 - ln4 + ln3) = (1/2)ln(3/2)##?
In the bracket with ##(ln2-ln4+ln3)## you can apply the following general rules of the logarithms:
1) ##lna+lnb=ln(a*b)##
2) ##lna-lnb=ln(a/b)##
and you should be able to get your result.
