# How do you condense ln5/2+ln6/2+ln7/2?

Dec 4, 2016

Using the exponential logarithm rule, $a \log b = \log {b}^{a}$, $\ln \frac{5}{2} + \ln \frac{6}{2} + \ln \frac{7}{2}$ can be written as

$\ln {5}^{\frac{1}{2}} + \ln {6}^{\frac{1}{2}} + \ln {7}^{\frac{1}{2}} = \ln \sqrt{5} + \ln \sqrt{6} + \ln \sqrt{7}$

Using the logarithmic multiplication rule, $\log a + \log b = \log a b$, $\ln \sqrt{5} + \ln \sqrt{6} + \ln \sqrt{7} = \ln \sqrt{210}$