Question

ALGUÉM ME AJUDA A RESOLVER
$log_{9}( \frac{1}{9} )$
$log_{25}(625)$
$log_{0.01}(10)$
$log_{4}( \frac{1}{2} )$
$log_{4}(\sqrt{2} )$
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Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{a)\:log_9\left(\dfrac{1}{9}\right) = log_9\:9^{-1} = -1\:.\:log_9\:9 = -1}$

$\mathsf{b)\:log_{25}\:625 = log_{25}\:25^2 = 2\:.\:log_{25}\:25 = 2}$

$\mathsf{c)\:log_{0,01}\:10 = log_{10^{-2}}\:10 = -\dfrac{1}{2}\:.\:log_{10}\:10 = -\dfrac{1}{2}}$

$\mathsf{d)\:log_4\left(\dfrac{1}{2}\right) = log_{2^2}\:2^{-1} = -\dfrac{1}{2}\:.\:log_2\:2 = -\dfrac{1}{2}}$

$\mathsf{e)\:log_{4}\:\sqrt{2} = log_{2^2}\:2^{\frac{1}{2}} = \dfrac{1}{4}\:.\:log_{2}\:2 = \dfrac{1}{4}}$