Resolva.... Pergunta de ideia deKjmaneiro

December 2019 1 163 Report

Resolva

$\log_5(0,000064)= \\ \\ \log_{49} \sqrt[3]{7} =$

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ArthurPDC a)
$\log_5(0,000064)=\log_5\left(\dfrac{64}{1000000}\right)=\log_5\left(\dfrac{2^6}{10^6}\right)\\\\
\log_5(0,000064)=\log_5\left(\dfrac{2^6}{(2\cdot5)^6}\right)=\log_5\left(\dfrac{2^6}{2^6\cdot5^6}\right)\\\\
\log_5(0,000064)=\log_5\left(\dfrac{1}{5^6}\right)\\\\
\log_5(0,000064)=\log_5(5^{-6})~~~\overline{\underline{\text{Propriedade: }\log_b(a^N)=N\cdot\log_b a}}\\\\
\log_5(0,000064)=-6\cdot \log_5(5)\\\\
\log_5(0,000064)=-6\cdot1\\\\
\boxed{\log_5(0,000064)=-6}
$

b)
$\log_{49}(\sqrt[3]{7})=\log_{49}(7^{\frac{1}{3}})~~~\overline{\underline{\text{Propriedade: }\log_b(a^N)=N\cdot\log_b a}}\\\\
\log_{49}(\sqrt[3]{7})=\dfrac{1}{3}\cdot\log_{49}(7)\\\\
\log_{49}(\sqrt[3]{7})=\dfrac{1}{3}\cdot\log_{(7^2)}(7)~~~\overline{\underline{\text{Propriedade: }\log_{(b^N)}(a)=\dfrac{1}{N}\cdot\log_b a}} \\\\
\log_{49}(\sqrt[3]{7})=\dfrac{1}{3}\cdot\dfrac{1}{2}\cdot\log_7(7)\\\\
\log_{49}(\sqrt[3]{7})=\dfrac{1}{3}\cdot\dfrac{1}{2}\cdot1\\\\
\boxed{\log_{49}(\sqrt[3]{7})=\dfrac{1}{6}}$

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