Question

Determine o valor de x pata que a expressão 2•2×=⁶√8• ⁴√2•⁶√2 se torne na verdade:

Answer 1

Resposta:

Explicação passo a passo:

$2\:.\:2^{x} =\sqrt[6]{8}\:.\:\sqrt[4]{2}\:.\:\sqrt[6]{2}$

$2^{(x+1)} =\sqrt[6]{2^{3} }\:.\:\sqrt[4]{2}\:.\:\sqrt[6]{2}$

$2^{(x+1)} =2^{\frac{3}{6} }\:.\:2^{\frac{1}{4} }\:.\:2^{\frac{1}{6} }$

$2^{(x+1)} =2^{(\frac{3}{6} +\frac{1}{4}+\frac{1}{6}) }$

$2^{(x+1)} =2^{(\frac{6}{12}+\frac{3}{12}+\frac{2}{12}) }$

$2^{(x+1)} =2^{\frac{11}{12} }$

 $x+1=\frac{11}{12}$

 $x=\frac{11}{12}-1$

 $x=\frac{11}{12}-\frac{12}{12}$

 $x=\frac{11-12}{12}$

 $x=-\frac{1}{12}$