Find a solution for the equation e^2x + 3*e^x = 10

The equation `e^(2x) + 3*e^x = 10` has to be solved for
x.

`e^(2x)` can be rewritten as `(e^x)^2`
.

The equation now be written
as:

`(e^x)^2 + 3*e^x = 10`

`(e^x)^2 +
3*e^x - 10 = 0`

`(e^x)^2 + 5*e^x - 2e^x - 10 =
0`

`(e^x)(e^x + 5) - 2(e^x + 5) =
0`

`(e^x - 2)(e^x + 5) = 0`

`e^x - 2 =
0`

`e^x = 2`

x = ln
2

`e^x + 5 = 0`

`e^x =
-5`

This is not possible as e is a positive number and the power of
a positive number is always positive.

The solution of the equation
`e^(2x) + 3*e^x = 10` is x = ln 2