Question

Alguém pode me ajudar a resolver a pergunta n2?

Answer 1

Explicação passo-a-passo:

$a = log_{11}(121) \\ b = log_{ \frac{1}{13} }( \frac{1}{169} ) \\ log_{b}(c) = - a$

$a = \frac{ log(121) }{ log(11) } \\ b = \frac{ log( \frac{1}{169} ) }{ log( \frac{1}{13} ) }$

$a = \frac{ log( {11}^{2} ) }{ log(11) } \\ b = \frac{ log( \frac{1}{ {13}^{2} } ) }{ log( \frac{1}{13} ) } = \frac{ log( {13}^{ - 2} ) }{ log( {13}^{ - 1} ) }$

$a = \frac{2 log(11) }{ log(11) } = 2 \\ b = \frac{ - 2 log(13) }{ - 1 log(13) } = 2$

$log_{b}(c) = - a \\ log_{2}(c) = - 2 \\ \frac{ log(c) }{ log(2) } = - 2 \\ log(c) = - 2 log(2) \\ log(c) = log( {2}^{ - 2} ) \\ log(c) = log( \frac{1}{ {2}^{2} } ) \\ log(c) = log( \frac{1}{4} ) \\ c = \frac{1}{4}$