What is the solution of ln(x-2)^2=6?

We will solve for
x
using the very basic properties of natural logarithms. I'll illustrate it below.
Explanation:
We have,
ln
(
x
−
2
)
2
=
6
Using the property,
ln
m
n
=
n
ln
m
,
We have,
ln
(
x
−
2
)
2
=
6
⇒
2
ln
(
x
−
2
)
=
6

⇒
ln
(
x
−
2
)
=
3

⇒
x
−
2
=
e
3
In the last step, we used the concept of inverse of the natural logarithms,
ln
m
=
n
⇒
m
=
e
n
Thus,
x
=
e
3
+
2
Where e is the base of natural logarithms.

Source: socratic.org