Question

1) Desenvolver aplicando as propriedades de logaritmo.

a)
$log_{2}( \frac{2ab}{c} )$
b)
$log_{3}( \frac{a ^{3}b {}^{2} }{ {c}^{4} } )$
c)
$log_{5}( \frac{5a}{bc} )$
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Answer 1

Resposta:

a)

$log_{2}( \frac{2ab}{c} ) = log_{2}(2) + log_{2}(a) + log_{2}(b) - log_{2}(c) = 1 + log_{2}(a) + log_{2}(b) - log_{2}(c)$

b)

$log_{3}( \frac{a ^{3}b {}^{2} }{ {c}^{4} } ) = log_{3}( {a}^{3} ) + log_{3}( {b}^{2} ) - log_{3}( {c}^{4} ) = 3 log_{3}(a) + 2 log_{3}(b) - 4 log_{3}(c)$

c)

$log_{5}( \frac{5a}{bc} ) = log_{5}(5) + log_{5}(a) - (log_{5}(b) + log_{5}(c) ) = 1 + log_{5}(a) - log_{5}(b) - log_{5}(c)$