Chapter 4.3, Problem 45E

To determine

To find: The function of the form $y={\log }_{a}x$ for the given graph.

Answer to Problem 45E

The function of the form $y={\log }_{a}x$ for the given graph is equal to $y={\log }_{5}x$ .

Explanation of Solution

Given information:

The graph of the function is shown below:

  

Calculation:

As shown in the graph, the function of type $y={\log }_{a}x$ passes through the point $\left(5,1\right)$ .

Substitute $5$ for $x$ and $1$ for $y$ in the function.

  $\begin{array}{c}y={\log }_{a}x\\ 1={\log }_{a}5\\ a^1=a^{{\log }_{a}5}\\ a=5\end{array}$

Substitute $5$ for $a$ in the function.

  $\begin{array}{c}y={\log }_{a}x\\ y={\log }_{5}x\end{array}$

Therefore, the function of the form $y={\log }_{a}x$ for the given graph is equal to $y={\log }_{5}x$ .