Question

Alguien me ayuda a comprobar el resultado?
El tema es ecuaciones exponenciales :p
${e}^{2x} - {e}^{x + 2} = {e}^{x + 1} - {e}^{3}$
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Answer 1

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$\bf\green{Resolvemos:}$

${e}^{2x} - {e}^{x + 2} = {e}^{x + 1} - {e}^{3}$

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

${t}^{2} - {te}^{2} = te - {e}^{3}$

$t = {e}^{2} \\ t = e \: \: \:$

${e}^{x} = {e}^{2} \\ {e}^{x} = e \: \:$

$x = 2 \\ x = 1$

$x_{1} = 1, x_{2} = 2$