O valor de log base 4 (2sobre log 4 na base 16) .... Pergunta de ideia deDanielR49

October 2020 1 108 Report

O valor de log base 4 (2sobre log 4 na base 16)

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Niiya

Verified answer

$\boxed{log_{4}(\frac{2}{log_{16}4})}$

Primeiro vamos resolver log de 4 na base 16:

$log_{16}(4)=x\\16^{x}=4\\(4^{2})^{x}=4^{1}\\4^{2x}=4^{1}\\2x=1\\x=1/2$
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$log_{4}(\frac{2}{log_{16}4})=log_{4}(\frac{2}{(1/2)})\\\\log_{4}(\frac{2}{log_{16}4})=log_{4}(2*\frac{2}{1})\\\\log_{4}(\frac{2}{log_{16}4})=log_{4}(4)\\\\\boxed{\boxed{\log_{4}(\frac{2}{log_{16}4})=1}}$

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