Chapter 5, Problem 24RE

(a)

To determine

To evaluate : The value of $f\left(1\right)$

Explanation of Solution

Given: The function is $f\left(x\right)=3^x$ and $g\left(x\right)={\log }_{3}x$ .

The value of $f\left(1\right)$ is calculated as,

  $\begin{array}{c}f\left(1\right)=3^1\\ =3\end{array}$

Therefore, the value of $f\left(1\right)$ is $3$ .

(b)

To determine

To evaluate : The value of $g\left(81\right)$

Explanation of Solution

Given: The function is $f\left(x\right)=3^x$ and $g\left(x\right)={\log }_{3}x$ .

The value of $g\left(81\right)$ is calculated as,

  $\begin{array}{c}g\left(81\right)={\log }_3\left(81\right)\\ =\frac{\log 81}{\log 3}\\ =4\end{array}$

Therefore, the value of $g\left(81\right)$ is $4$ .

(c)

To determine

To evaluate : The value of $f\left(-4\right)$

Explanation of Solution

Given: The function is $f\left(x\right)=3^x$ and $g\left(x\right)={\log }_{3}x$ .

The value of $f\left(-4\right)$ is calculated as,

  $\begin{array}{c}f\left(-4\right)=3^{-4}\\ =\frac{1}{3^4}\\ =\frac{1}{81}\end{array}$

Therefore, the value of $f\left(-4\right)$ is $\frac{1}{81}$ .

(d)

To determine

To evaluate : The value of $g\left(\frac{1}{243}\right)$

Explanation of Solution

Given: The function is $f\left(x\right)=3^x$ and $g\left(x\right)={\log }_{3}x$ .

The value of $g\left(\frac{1}{243}\right)$ is calculated as,

  $\begin{array}{c}g\left(\frac{1}{243}\right)={\log }_3\left(\frac{1}{243}\right)\\ =\frac{\log \frac{1}{243}}{\log 3}\\ =-5\end{array}$

Therefore, the value of $g\left(\frac{1}{243}\right)$ is $-5$ .