Question

Halle el valor de x​

Answer 1

Respuesta:

x = 9

Explicación paso a paso:

se sabe que:

${x}^{a} .{x}^{b} ={x}^{a+b}$

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$\sqrt[7]{ \frac{ {5}^{16} + {5}^{2} }{ {5}^{x} + {5}^{2} } } = 5$

$\frac{ {5}^{16} + {5}^{x} }{ {5}^{x} + {5}^{2} } = {5}^{7}$

${5}^{16} + {5}^{x} = {5}^{7} ( {5}^{x} + {5}^{2} )$

${5}^{16} + {5}^{x} = {5}^{7} ( {5}^{x}) + {5}^{7} ( {5}^{2} )$

${5}^{16} + {5}^{x} ={5}^{x + 7} + {5}^{7 + 2}$

${5}^{16} + {5}^{x} ={5}^{x + 7} + {5}^{9}$

${5}^{16} - {5}^{9} ={5}^{x + 7} - {5}^{x}$

${5}^{16} - {5}^{9} ={5}^{x}\cdot {5}^{7} - {5}^{x}$

${5}^{16} - {5}^{9} ={5}^{x}({5}^{7} - 1)$

$\frac{{5}^{16} - {5}^{9} }{ {5}^{7} - 1 } ={5}^{x}$

$\frac{{5}^{9 + 7} - {5}^{9} }{ {5}^{7} - 1 } ={5}^{x}$

$\frac{{5}^{9} \cdot {5}^{7} - {5}^{9} }{ {5}^{7} - 1 } ={5}^{x}$

$\frac{{5}^{9} ({5}^{7} -1)}{ {5}^{7} - 1 } ={5}^{x}$

$\frac{{5}^{9} ({5}^{7} -1)}{ ({5}^{7} - 1 )} ={5}^{x}$

${5}^{9} = {5}^{x}$

$9 = x$

Answer 2

Respuesta:

es 9 jaja hola

Explicación paso a paso: