Question

Resolva as seguintes equações exponenciais.

Answer 1

Explicação passo-a-passo:

b) $\sf (\sqrt{3})^x=\sqrt[3]{81}$

$\sf (3^{\frac{1}{2}})^x=\sqrt[3]{3^4}$

$\sf 3^{\frac{x}{2}}=3^{\frac{4}{3}}$

$\sf \dfrac{x}{2}=\dfrac{4}{3}$

$\sf 3x=2\cdot4$

$\sf 3x=8$

$\sf x=\dfrac{8}{3}$

$\sf S=\left\{\dfrac{8}{3}\right\}$

c) $\sf (\sqrt[3]{2})^x=8$

$\sf (2^{\frac{1}{3}})^x=2^3$

$\sf 2^{\frac{x}{3}}=2^3$

$\sf \dfrac{x}{3}=3$

$\sf x=3\cdot3$

$\sf x=9$

$\sf S=\{9\}$

d) $\sf (\sqrt[4]{3})^x=\sqrt[3]{9}$

$\sf (3^{\frac{1}{4}})^x=\sqrt[3]{3^2}$

$\sf 3^{\frac{x}{4}}=3^{\frac{2}{3}}$

$\sf \dfrac{x}{4}=\dfrac{2}{3}$

$\sf 3x=4\cdot2$

$\sf 3x=8$

$\sf x=\dfrac{8}{3}$

$\sf S=\left\{\dfrac{8}{3}\right\}$