Chapter 8, Problem 40SGR

To determine

To find: The approximate value of the expression ${\log }_{5}64$ .

Answer to Problem 40SGR

The solution of the expression is $2.5841$ .

Explanation of Solution

Given:

The expression is ${\log }_{5}64$ .

Calculation:

Simplify the expression ${\log }_{5}64$ by using Product Rule as follows.

  $\begin{array}{c}{\log }_{5}64={\log }_5\left(16\cdot 4\right)\\ ={\log }_{5}16+{\log }_{5}4\\ ={\log }_{5}16+{\log }_5{2}^2\\ ={\log }_{5}16+2{\log }_{5}2\end{array}$

Simplify further.

  $\begin{array}{c}{\log }_{5}64\approx 1.7227+2\left(0.4307\right)\\ \approx 2.5841\end{array}$

Therefore, the solution of the expression is $2.5841$ .