Question

QUESTÃO 03 – Calcule:
a)    log⅔ 8 sobre 27
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Answer 1

Resposta:

$\boxed{\log_{\dfrac{2}{3}}\dfrac{8}{27}=\bf{3}}$

Explicação passo-a-passo:

A definição de log é:

$O\ log\ de\ um\ valor\ \'{e}\ a\ base\ do\ log\ elevado\ ao\ seu\ resultado, ent\~{a}o:\\\\\log_{A}B=C\ \'{e}\ A^C =B\\\\\log_{\dfrac{2}{3}}\dfrac{8}{27}=k\\\dfrac{8}{27}={\left(\dfrac{2}{3}\right)}^k\\\\\dfrac{2^3}{3^3}={\left(\dfrac{2}{3}\right)}^k\\\\\left(\dfrac{2}{3}\right)^3={\left(\dfrac{2}{3}\right)}^k\\\\\\k=3\\\\\boxed{\log_{\dfrac{2}{3}}\dfrac{8}{27}=\bf{3}}$

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