Question

Função Exponencial: resolva a equação
${4}^{x - 1}$
=
$\frac{1}{ \sqrt{2} }$

​

Answer 1

Olá, siga a explicação:

Propriedades do expoentes:

$\sf 2(x-1) = -\dfrac{1}{2}$

Resolver:

$\sf 2(x-1) = - \dfrac{1}{2} : \: \: \: x= \dfrac{3}{4}$

Ou seja:

$\boxed {x = \dfrac{3}{4} }$

• Att. MatiasHP

Answer 2

Olá,

$\tt \: {4}^{x - 1} = \frac{1}{ \sqrt{2} } \\ \tt \: \left( {2}^{2} \right ){}^{x - 1} = \frac{1}{ {2}^{ \frac{1}{2} } } \\ \tt \: {2}^{2x - 2} = {2}^{ - \frac{1}{2} } \\ \tt \: { \cancel{2}}^{2x - 2} = { \cancel{2}}^{ - \frac{1}{2} } \\ \tt \: 2x - 2 = - \frac{1}{2} \\ \tt \: 2x = - \frac{1}{2} + 2 \\ \tt \: 2x = - \frac{1}{2} + \frac{4}{2} \\ \tt \: 2x = \frac{3}{2} \\ \tt \: x = \frac{3}{2} \cdot \: \frac{1}{2} \\ \tt \: x = \frac{3}{4}$