Chapter 8.3, Problem 3ACYP

To determine

To Evaluate: The expression.

Answer to Problem 3ACYP

  ${\log }_{3}81=4$

Explanation of Solution

Given: ${\log }_{3}81$

Formula used:

  $\begin{array}{l}{\log }_{b}x=yifandonlyif\\ b^y=x\end{array}$

Given: ${\log }_{3}81$

Let the expression is equals to $y$

Then

Using the logarithm form

  ${\log }_{b}x=yif{b}^y=x$

  $\begin{array}{l}{\log }_{3}81=y\\ b=3,x=81\\ then\\ 3^y=81\\ 3^y=3^4\\ y=4\\ {\log }_{3}81=4\end{array}$

Hence, ${\log }_{3}81=4$