Chapter 4.5, Problem 1GP

Solution

To evaluate: The given logarithmic expression.

  $-0.263$

Given:

An expression ${\log }_6\frac{5}{8}$.

Concept used:

If $b,m$ and $n$ are positive numbers then ${\log }_b\frac{m}{n}={\log }_{b}m-{\log }_{b}n$ where $b\ne 1$.

Calculation:

  ${\log }_6\frac{5}{8}$

Use the quotient property.

  $\begin{array}{c}{\log }_6\frac{5}{8}={\log }_{6}5-{\log }_{6}8\\ =0.898-1.161\\ =-0.263\end{array}$

Conclusion:

The evaluation of the logarithmic expression ${\log }_6\frac{5}{8}$ gives $-0.263$.