Question

qual o valor de x???? me ajudem por favor!!!!!
$\sqrt[x]{ \frac{36}{49} } = \sqrt[6]{ \frac{216}{343} }$
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Answer 1

Explicação passo-a-passo:

$\sqrt[x]{ \frac{36}{49} } = \sqrt[6]{ \frac{216}{343} }$

$\sqrt[x]{ \frac{ {6}^{2} }{ {7}^{2} } } = \sqrt[6]{ \frac{ {6}^{3} }{ {7}^{3} } }$

$\sqrt[x]{( \frac{6}{7} {)}^{2} } = \sqrt[6]{( \frac{6}{7} {)}^{3} }$

Temos que:

$\sqrt[n]{ {a}^{m} } = {a}^{ \frac{m}{n} }$

$( \frac{6}{7} {)}^{ \frac{2}{x} } = ( \frac{6}{7} {)}^{ \frac{3}{6} }$

Se:

${a}^{n} = {a}^{m} = > n = m$

Então,

$\frac{2}{x} = \frac{3}{6}$

$3x = 12$

$x = \frac{12}{3}$

$x = 4$