Question

El valor de "x" en:
a) 5 b)0 c)1 d) 4 e)9​

Answer 1

$\sqrt[ {5}^{x} ]{ {2}^{( {5}^{3x - 8)} } } = {128}^{ {7}^{2x - 9} } \\ {2}^{ \frac{ {5}^{3x - 8} }{ {5}^{x} } } = {( {2}^{7})}^{ {7}^{2x - 9} } \\ {2}^{ {5}^{3x - 8 - x} } = {2}^{7. {7}^{2x - 9} } \\ {2}^{ {5}^{2x - 8} } = {2}^{ {7}^{2x - 9 + 1} } \\ {2}^{ {5}^{2x - 8} } = {2}^{ {7}^{2x - 8} } \\ {5}^{2x - 8} = {7}^{2x - 8} \\ {5}^{2x} . {5}^{ - 8} = {7}^{2x} . {7}^{ - 8} \\ {5}^{2x} . \frac{1}{ {5}^{8} } = {7}^{2x} . \frac{1}{ {7}^{8} } \\ \frac{ {5}^{2x} }{ {5}^{8} } = \frac{ {7}^{2x} }{ {7}^{8} } \\ \frac{ {5}^{2x} }{ {7}^{2x} } = \frac{ {5}^{8} }{ {5}^{2x} } \\ {( \frac{5}{7} )}^{2x} = {( \frac{5}{7}) }^{8} \\ 2x = 8 \\ x = 4$

Respuesta: D) 4