Question #c2837

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Question #c2837

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Answer 1 · 2016-09-19T19:39:57

$x = \frac{1}{2}$ $x=color(green)(1/2)$

Explanation:

If
$XXX 10 x e^{x} - 5 e^{x} = 0$ $color(white)("XXX")10xe^x-5e^x=0$
since
$XXX e^{any power} > 0$ $color(white)("XXX")e^"any power" > 0$

We can divide (both sides of)the given equation by $5 e^{x}$ $5e^x$ to get
$XXX 2 x - 1 = 0$ $color(white)("XXX")2x-1=0$

From which we can see that
$XXX x = \frac{1}{2}$ $color(white)("XXX")x=1/2$

Answer 2 · 2016-09-19T19:42:08

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

Explanation:

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

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

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

but $e^{x} \neq 0 thus no solution$ $e^x≠0" thus no solution"$

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

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Question #c2837

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