Answer
The graph is shown below.
Work Step by Step
The function $f\left( x \right)={{\log }_{5}}x$ can be written as ${{5}^{y}}=x$.
Substitute $y=0,1,2,-1,-2$ in the function ${{5}^{y}}=x$ and tabulate the values as shown in Table 1.
$\begin{matrix}
{{5}^{y}}=x & y \\
1 & 0 \\
5 & 1 \\
25 & 2 \\
\frac{1}{5} & -1 \\
\frac{1}{25} & -2 \\
\end{matrix}$
Plot these points and connect them with a smooth curve as shown below in Figure 1.
