Answer
please see image
.
Work Step by Step
1. The inequality sign is $\geq $, so we draw a solid border
2. The border, $y=\log_{3}(\mathrm{x}-1)$
is a logarithmic function, base $3 > 1,$
It is obtained from $\log_{3}x$ by shifting left by one unit.
The function is defined only for $x>1.$
This means that its vertical asymptote, $x=1$
will not be included in the solution, and will be a border.
We graph it with a dashed line (not included)
and will shade only to the right of the asymptote.
Plot some points (see table)
and join with a smooth (solid) curve
3. We ca$\mathrm{n}^{\prime}$t test the point $(0,0)$, as the inequality defined only for $x>1.$
We test (10,0)
$ 0 \geq \log_{3}(10-1)\quad ?$
$0 \geq \log_{3}9\quad ?$
$0 \geq 2\quad ?$
No.
4. Shade the region that the point (10,0) does not belong to.
Also, apply the observation about the vertical asymptote
