#### Answer

See below:

#### Work Step by Step

Let us draw the graph of the function $f\left( x \right)=\ln x$ and $g\left( x \right)=\ln \left( x-2 \right)+1$ as follows:
Step 1:
Find the $x\text{-intercept}$ and $y\text{-intercept}$ as follows:
Consider the function $f\left( x \right)=\ln x$
$\left( 1,0 \right)$ is the only $x\text{-intercept}$
And consider the function $g\left( x \right)=\ln \left( x-2 \right)+1$.
$\left( 2.3678,0 \right)$ is the intercept, where 2.3678 is the approximate value of $\frac{1}{e}+2$.
Step 2:
Plot the intercept on the rectangular plane.
Step 3:
Use a smooth curve along its asymptotes and draw the curve.
The graph of the function $f\left( x \right)=\ln x$ intersects the x-axis at the point $\left( 1,0 \right)$.