# Question c2837

Sep 19, 2016

$x = \textcolor{g r e e n}{\frac{1}{2}}$

#### Explanation:

If
$\textcolor{w h i t e}{\text{XXX}} 10 x {e}^{x} - 5 {e}^{x} = 0$
since
color(white)("XXX")e^"any power" > 0

We can divide (both sides of)the given equation by $5 {e}^{x}$ to get
$\textcolor{w h i t e}{\text{XXX}} 2 x - 1 = 0$

From which we can see that
$\textcolor{w h i t e}{\text{XXX}} x = \frac{1}{2}$

Sep 19, 2016

$x = \frac{1}{2}$

#### Explanation:

There is a common factor of ${e}^{x}$ which can be taken out.

$\Rightarrow {e}^{x} \left(10 x - 5\right) = 0$

$\Rightarrow {e}^{x} = 0 , 10 x - 5 = 0$

but e^x≠0" thus no solution"#

and $10 x - 5 = 0 \Rightarrow x = \frac{1}{2} \text{ is the only solution}$