Chapter 8.6, Problem 57PPS

To determine

To find: The value of given expression.

Answer to Problem 57PPS

The value of given expression is $1.2343$ .

Explanation of Solution

Given information:

The expression is ${\log }_5{\left(2.7\right)}^2$ .

Calculation:

Consider the property.

  ${\log }_{a}n=\frac{{\log }_{b}n}{{\log }_{b}a}$

Consider the expression.

  $\begin{array}{c}{\log }_5{\left(2.7\right)}^2=\frac{{\log }_{10}7.29}{{\log }_{10}5}\\ =\frac{\log 7.29}{\log 5}\\ =1.2343\end{array}$