How do you use the properties of logarithms to expand lnroot3(t)?

Jul 10, 2017

$\ln \sqrt[3]{t} = \frac{1}{3} \ln t$

Explanation:

One of the property of logarithm is that ${\log}_{a} {x}^{m} = m {\log}_{a} x$

Hence $\ln \sqrt[3]{t} = \ln {t}^{\frac{1}{3}} = \frac{1}{3} \ln t$

Note that $\ln x$ is nothing but ${\log}_{e} x$.