Chapter EP, Problem 8.3.11EP

To determine

The value of logarithmic expression.

Explanation of Solution

Given information:

The given equation is ${\log }_6{6}^5$

Calculations:

To convert the logarithmic function into exponential function, we should know the concept below.

Let $b$ and $x$ be positive numbers with $b\ne 0$ . The logarithm of x with base b is denoted is denoted by ${\log }_{b}x$ and is defined as exponent $y$ that makes the equation $b^y=x$ true.

  

Following the rule we can convert the equation in exponential form. Then we can find the value of the expression.

  $\begin{array}{l}{\log }_6{6}^5=y\\ 6^y=6^5\\ \text{comparing both sides we can write,}\\ y=5\\ Thus,\\ {\log }_6{6}^5=5\end{array}$