Question

qual o valor de x na igualdade?
{me ajudem pvffff}


$\sqrt[16]{2^8}$=$\sqrt[x]{2^4} }$

Answer 1

$\large{ \orange{ \boxed{ \boxed{ \tt \: \green{x = 8}}}}}$

Solução

$\large{ \tt \sqrt[16]{ {2}^{8} } = \sqrt[x]{ {2}^{4} } }$

Lembre-se da definição de raiz:

$\large{ \orange{ \boxed{ \blue{ \tt\sqrt[n]{ {x}^{m} } = {x}^{ \frac{ m}{n} } } }}}$

Aplicando essa definição:

$\large{ \tt \red{\overbrace{\blue{ \sqrt[16]{ {2}^{8} } } } ^{ {2}^{ \frac{8}{16} } } }} = \tt \red{\underbrace{ \green{ \sqrt[x]{ {2}^{4} } }}_{ {2}^{ \frac{4}{x} } }}$

$\large{ \orange{ \tt \: {2}^{ \frac{8}{16} } = {2}^{ \frac{4}{x} } }} \\ \\ \large{ \orange{ \tt \: { \cancel2}^{ \frac{8}{16} } = { \cancel2}^{ \frac{4}{x} } }} \\ \\ \tt \large\orange{\iff \: \frac{8}{16} = \frac{4}{x} } \\ \\ \tt \large{ \orange{8x = 4 \cdot16}} \\ \\ \tt \large{ \orange{8x = 64}} \\ \\ \tt \large{ \orange{x = \frac{64}{8} }} \\ \\ \tt \large{ \orange{ \therefore \: x = 8}}$