# Question 6d75a

Mar 21, 2017

$x = 1$

#### Explanation:

$e = \left({e}^{3 x}\right) \left(\frac{1}{e} ^ 2\right)$

$e \cdot {e}^{2} = {e}^{3 x}$

${e}^{3} = {e}^{3 x}$

therefore,
$3 = 3 x$
$\frac{3}{3} = x$
$1 = x$

Mar 21, 2017

(Solving the equation written in the title of this question):
$\textcolor{\mathrm{da} r k g r e e n}{e = {e}^{3 x} \cdot \left(\frac{1}{{e}^{2}}\right)}$

$e = \left({e}^{3 x}\right) \left({e}^{- 2}\right)$

$e = {e}^{3 x - 2}$

$3 x - 2 = 1$

$3 x = 3$

$\textcolor{\mathrm{da} r k g r e e n}{x = 1}$
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(Solving the equation written in the description of this question):
color(darkblue)((e^(x^2)=e^(3x)*(1/(e^2)))#

${e}^{{x}^{2}} = {e}^{3 x - 2}$

${x}^{2} = 3 x - 2$

${x}^{2} - 3 x + 2 = 0$
${x}^{2} - x - 2 x + 2 = 0$
$\left(x - 2\right) \left(x - 1\right) = 0$

$\textcolor{\mathrm{da} r k b l u e}{x = 2 , x = 1}$