How do you prove that $(\frac{1}{2}) (ln 2 - ln 4 + ln 3) = (\frac{1}{2}) ln (\frac{3}{2})$ $(1/2)(ln2 - ln4 + ln3) = (1/2)ln(3/2)$ ?

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Answer 1 · 2015-02-02T11:36:07

In the bracket with $(ln 2 - ln 4 + ln 3)$ $(ln2-ln4+ln3)$ you can apply the following general rules of the logarithms:

1) $ln a + ln b = ln (a \cdot b)$ $lna+lnb=ln(a*b)$

2) $ln a - ln b = ln (\frac{a}{b})$ $lna-lnb=ln(a/b)$

and you should be able to get your result.

How do you prove that (12)(ln2−ln4+ln3)=(12)ln(32)(1/2)(ln2 - ln4 + ln3) = (1/2)ln(3/2)?