Example 4.3.4 (A nice equation)
We solve the equation
.
Let
, where
. Then:

We have now:
 We take care of the second equation:
 We substitute into the first equation:

. This equation has no real solution.

. This
equation is equivalent to
Its (real) solutions are
and
.

. This equation has no solution.
In conclusion, the complex solutions of the equation
are:
and 

Example 4.3.5 (A nice equation  second way)
We solve the equation
.
We substitute
and solve for
the equation
. The solutions are:
and
. In order to find the corresponding values of
, we need logarithms. They will be defined in the next paragraph
(v.i.
4). This exercise will be finished in example
4.6.