Question

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Veja:
$\large\sf{}Calcule \: a \: expressão \: a \: seguir:$
$\Large\sf{}L = \dfrac{ log_{4}(81) \div log_{4}(162) }{ log_{9}(3) \div log_{9}(162) }$
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Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\sf L = \dfrac{log_4(81) \div log_4(162)}{log_9(3) \div log_9(162)}$

$\sf L = \dfrac{log_4(81)}{log_4(162)}\:.\:\dfrac{log_9(162)}{log_9(3)}$

$\sf L = \dfrac{log_{2^2}(3^4)}{log_{2^2}(2\:.\:3^4)}\:.\:\dfrac{log_{3^2}(2\:.\:3^4)}{log_{3^2}(3)}$

$\sf L = \dfrac{\dfrac{4\:.\:log_{2}(3)}{2}}{\dfrac{log_{2}(2) + 4\:.\:log_2(3)}{2}}\:.\:\dfrac{\dfrac{log_{3}(2) + 4\:.\:log_3(3)}{2}}{\dfrac{log_{3}(3)}{2}}$

$\sf L = \dfrac{4\:.\:log_{2}(3)}{1 + 4\:.\:log_2(3)}\:.\:[\:log_{3}(2) + 4\:]$

$\sf L = \dfrac{4 + 16\:.\:log_{2}(3)}{1 + 4\:.\:log_2(3)}$

$\sf L = \dfrac{log_2(3^4) +log_{2}(3^{16})}{log_2(3) + log_2(3^4)}$

$\sf L = \dfrac{log_2(3^{20})}{log_2(3^5)}$

$\sf L = \dfrac{20}{5}\:.\:\dfrac{log_2(3)}{log_2(3)}$

$\boxed{\boxed{\sf L = 4}}$