Question

resolva a seguinte equação exponencial:

$( \sqrt[4]{3}) {}^{x} = \sqrt[3]{9}$
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Answer 1

Resposta:

$x=\frac{8}{3}$

Explicação passo-a-passo:

$(\sqrt[4]{3}) {}^{x} = \sqrt[3]{9}\\\\(3^{\frac{1}{4}})^{x}=\sqrt[3]{3^{2}}\\\\3^{\frac{x}{4}}={3^{\frac{2}{3}}}\\\\\frac{x}{4}=\frac{2}{3}\\\\x=\frac{8}{3}$

Propriedades:

$(a^{m})^{n}=a^{m.n}\\\\\sqrt[n]{x^m} =x^{\frac{m}{n} }\\\\a^{m}a^{n}=a^{m+n}\\\\\frac{a^{m}}{a^{n}}=a^{m-n} \\\\a^{0}=1\\\\a^{1}=a$