How do you condense ln2 + ln6 - (1/2)ln9?

Jul 30, 2016

$\ln 2 + \ln 6 - \left(\frac{1}{2}\right) \ln 9 = \ln 4$

Explanation:

We can use $\ln x + \ln y = \ln x y$, $\ln x - \ln y = \ln \left(\frac{x}{y}\right)$ and $\frac{1}{n} \ln x = \ln \left(\sqrt[n]{x}\right)$

Hence, $\ln 2 + \ln 6 - \left(\frac{1}{2}\right) \ln 9$

= $\ln \left(2 \times 6\right) - \ln \left(\sqrt{9}\right)$

= $\ln 12 - \ln 3$

= $\ln \left(\frac{12}{3}\right) = \ln 4$