Question

Determine o valor do número x em cada uma das igualdades

Answer 1

Resposta:

e) x = 4

f) x = 3

Explicação passo a passo:

e)

$\sqrt[x]{\sqrt[6]{10} } =\sqrt[24]{10} \\\\\sqrt[x]{10^{\frac{1}{6} } }=10^{\frac{1}{24} } \\\\10^{\frac{1}{6}:x } =10^{\frac{1}{24}$

$\frac{1}{6}:x=\frac{1}{24} \\\\\frac{1}{6x}=\frac{1}{24}\\\\6x=24\\\\x=\frac{24}{6}\\\\x=4$

$f)\sqrt[5]{\sqrt[x]{3} } =\sqrt[15]{3} \\\\\sqrt[5]{3^{\frac{1}{x} } } =3^{\frac{1}{15} } \\\\3^{\frac{1}{x}:5}=3^{\frac{1}{15} } \\\\\frac{1}{5x}=\frac{1}{15} \\\\5x=15\\\\x=\frac{15}{5}\\\\x=3$

Outro modo

$\sqrt[x]{\sqrt[6]{10} }=\sqrt[24]{10} \\\\\sqrt[6x]{10}=\sqrt[24]{10} \\\\6x=24\\\\x=\frac{24}{6}\\\\x=4 \\\\f)\sqrt[5]{\sqrt[x]{3} } =\sqrt[15]{3} \\\\\sqrt[5x]{3} =\sqrt[15]{3} \\\\5x=15\\\\x=\frac{15}{5}\\\\x=3$