1. ## Exponential Equation

How to solve:

2. Hello, thebristolsound!

Solve: . $e^{2x} + 3e^x - 10 \:=\:0$

Factor: . $(e^x + 5)(e^x - 2) \:=\:0$

Set each factor equal to zero and solve.

. . $e^x + 5 \:=\:0 \quad\Rightarrow\quad e^x \:=\:-5$ . . . no real roots

. . $e^x - 2 \:=\:0 \quad\Rightarrow\quad e^x \:=\:2 \quad\Rightarrow\quad\boxed{ x \:=\:\ln 2}$

3. hello
u can also put $e^{x}=u$ and solve for $u$,
$u^2+3u-10=0$

4. Following on from Soroban you can also have complex roots:

$
(e^x + 5)(e^x - 2) \:=\:0
$

$
e^x = - 5
$

$x = ln(5)+ i\pi$