Question

Resolva a equação e^2x-3.e^x+2=0, dados log2=0,3 e loge = 0,43

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

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

$\sf{y = e^x}$

$\sf{y^{2} - 3y + 2 = 0}$

$\sf{\Delta = b^2 - 4.a.c}$

$\sf{\Delta = (-3)^2 - 4.1.2}$

$\sf{\Delta = 9 - 8}$

$\sf{\Delta = 1}$

$\sf{y = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{3 \pm \sqrt{1}}{2} \rightarrow \begin{cases}\mathsf{y' = \dfrac{3 + 1}{2} = \dfrac{4}{2} = 2}\\\\\mathsf{y'' = \dfrac{3 - 1}{2} = \dfrac{2}{2} = 1}\end{cases}}$

$\sf{e^x = 2}$

$\sf{x = ln\:2}$

$\sf{e^x = 1}$

$\sf{e^x = e^0}$

$\sf{x = 0}$

$\boxed{\boxed{\sf{S = \{ln\:2;0\}}}}$