Question

o valor de log
1/625

Answer 1

Resposta:

[ E ] N.D.A

$\boxed{ \boxed{ \mathsf{ log\,\,_{\frac{ 1 }{ 625 } } \,\, \sqrt{ 5 } \,\, = \,\, -\dfrac{ 1 }{ 8 } } } } }$

Resolução:

Temos:

$\mathsf{log_{ \frac{ 1 }{ 625 } } \,\, \sqrt{ 5 } = x \,\,\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\,\,\,\, \bigg( \dfrac{ 1 }{ 625 } \bigg)^{ x } = \sqrt{ 5 } }$

Daí, vem:

$\mathsf{ \big( 625 \big)^{ -x } = 5^{ \frac{ 1 }{ 2 } } }\\ \\ \\ \mathsf{ \big( 5^4 \big)^{ -x } = 5^{ \frac{ 1 }{ 2 } } } \\ \\ \\ \\ \mathsf{ 5^{ -4x } = 5^{ \frac{ 1 }{ 2 } } } \\ \\ \\ \mathsf{ -4x = \dfrac{ 1 }{ 2 } }\\ \\ \\ \boxed{ \mathsf{ x = - \dfrac{ 1 }{ 8 } } }$