#### Answer

$x=\left\{0.01, 1.47\right\}$

#### Work Step by Step

To solve the given equation graphically, you have to treat each side of the equation as a function.
Thus, using a graphing utility, graph the functions:
$y=\log{x}$ (the blue graph)
$y=x^2-2$ (the red graph)
(refer to the image below for the graph.
The point/s where the graphs intersect are the points where $\log{x}=x^2-2$.
The x-coordinates of these point are the solutions to the given equation.
Note that the graphs intersect at the points $(0.01, -2)$ and $(1.472, 0.168)$.
The x-coordinates of these points are $0.01$ and $1.472$.
Rounded-off to two decimal places, the solution to the given equation is:
$x=\left\{0.01, 1.47\right\}$