Answer
The graph is shown below.
Work Step by Step
$y={{\log }_{2}}x$
The function $y={{\log }_{2}}x$ can be written as $x={{2}^{y}}$.
Substitute $y=0$ in $x={{2}^{y}}$:
$\begin{align}
& x={{2}^{0}} \\
& =1
\end{align}$
Substitute $y=1$ in $x={{2}^{y}}$:
$\begin{align}
& x={{2}^{1}} \\
& =2
\end{align}$
Substitute $y=2$ in $x={{2}^{y}}$:
$\begin{align}
& x={{2}^{2}} \\
& =4
\end{align}$
Substitute $y=-1$ in $x={{2}^{y}}$:
$\begin{align}
& x={{2}^{-1}} \\
& =\frac{1}{2}
\end{align}$
Substitute $y=-2$ in $x={{2}^{y}}$:
$\begin{align}
& x={{2}^{-2}} \\
& =\frac{1}{{{2}^{2}}} \\
& =\frac{1}{4}
\end{align}$
Tabulate the obtained values as shown below:
$\begin{matrix}
x & y \\
1 & 0 \\
2 & 1 \\
4 & 2 \\
\frac{1}{2} & -1 \\
\frac{1}{4} & -2 \\
\end{matrix}$
Now, draw the graph of $y={{\log }_{2}}x$