Question

desenvolva os logaritmos aplicando propriedade
$log_{2} \sqrt[2]{8 {}^{3} } =$
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Answer 1

Antes vou lembrar um conceito:

$a^{\frac{b}{c}} = \sqrt[c]{a^b} \\\\\log _{a} b^c=c\cdot log_{a} b\\\\\log _{a} b = x \implies a^x =b$

Agora a questão:

$log_{2} \sqrt[2]{8^3} = x\\\\log_{2} 8^{\frac{3}{2}} = x\\\\\dfrac{3}{2}\cdot log_{2} \:8 = x\\\\\dfrac{3}{2}\cdot log_{2} \:2^3 = x\\\\\dfrac{3}{2}\cdot 3\cdot log_{2} \:2 = x\\\\\dfrac{3}{2}\cdot 3 = x\\\\x= \dfrac{9}{2}=4.5$