Question

e^2x - 3 * e^× + 2 =0 . sendo log 2=0.30 e log e=0,43​
qual seria o valor de x?

Answer 1

${e}^{2x} - 3. {e}^{x} + 2 = 0 \\ {e}^{2x} - 3 {e}^{x} = - 2 \\ {({e}^{x}) }^{2} - 3 {e}^{x} = - 2 \\ faça \: {e}^{x} = k$

${k}^{2} - 3k = - 2 \\ {k}^{2} - 3k + 2 = 0$

$\Delta = {b}^{2} - 4ac \\ \Delta = {( - 3)}^{2} - 4.1.2 \\ \Delta = 9 - 8 \\ \Delta = 1$

$k = \frac{ - b± \sqrt{\Delta} }{2a} \\ k= \frac{ - ( - 3)± \sqrt{1} }{2.1} \\ k = \frac{3± 1}{2}$

$k' = \frac{3 + 1}{2} = \frac{4}{2} = 2 \\ k'' = \frac{3 - 1}{2} = \frac{2}{2} = 1$

Voltando

${e}^{x} = k \\ {e}^{x} = 2 \\ x = log_{e}(2) = \frac{ log(2) }{ log(e) }$

$x = \frac{0,30}{0,43} = 0,69$

${e}^{x} = k \\ {e}^{x} = 1 \\ x = log_{e}(1) = 0$