Question

aplicando a propriedade dos logaritmos, simplifique as expressões
a) log (64 • 13)
²
b)
$log_{3}(13.3)$
c)
$log_{ \binom{1}{4} }( \frac{1}{4} ) {}^{9}$



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Answer 1

Explicação passo-a-passo:

a )

$log_{2}(64 \times 13) = log_{2}(64) + log_{2}(13)$

$= log_{2}( {2}^{6} ) + log_{2}(13)$

$= 6 log_{2}(2) + log_{2}(13)$

$= 6(1) + log_{2}(13)$

$= 6 + log_{2}(13)$

b)

$log_{3}(3 \times 13) = log_{3}(3) + log_{3}(13)$

$= 1 + log_{3}(13)$

c)

$log_{ \frac{1}{4} }( \frac{1}{4} {)}^{9} = 9 log_{ \frac{1}{4} }( \frac{1}{4} ) = 9(1) = 9$