Answer
The value of ${{\log }_{a}}\frac{2}{7}$ is $-3.2698$.
Work Step by Step
${{\log }_{a}}\frac{2}{7}$
Apply the quotient rule for logarithms,
${{\log }_{a}}\frac{2}{7}={{\log }_{a}}2-{{\log }_{a}}7$
Substitute ${{\log }_{a}}2=1.8301\text{ and }{{\log }_{a}}7=5.0999$ to solve.
$\begin{align}
& {{\log }_{a}}\frac{2}{7}=1.8301-5.0999 \\
& =-3.2698
\end{align}$
Thus, the value of the logarithm ${{\log }_{a}}\frac{2}{7}$ is $-3.2698$.
