Question

Aplicando a propriedade dos logaritmos, simplifique a questão;

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log\left(\sqrt[3]{\dfrac{a^4\sqrt{ab}}{b^2\sqrt[3]{bc}}}\right)^2}$

$\mathsf{log\left(\sqrt[3]{\dfrac{a^{4}(ab)^{\frac{1}{2}}}{b^2(bc)^{\frac{1}{3}}}}\right)^2}$

$\mathsf{log\left(\sqrt[3]{\dfrac{a^{8}(ab)}{b^4(bc)^{\frac{2}{3}}}}\right)}$

$\mathsf{log\left(\dfrac{a^{\frac{8}{3}}(ab)^{\frac{1}{3}}}{b^{\frac{4}{3}}(bc)^{\frac{2}{9}}}\right)}$

$\mathsf{\dfrac{\dfrac{8}{3}\:log\:a + \dfrac{1}{3}\:log\:a + \dfrac{1}{3}\:log\:b }{\dfrac{4}{3}\:log\:b + \dfrac{2}{9}\:log\:b + \dfrac{2}{9}\:log\:c}}$

$\mathsf{\dfrac{\dfrac{9}{3}\:log\:a + \dfrac{1}{3}\:log\:b }{\dfrac{14}{9}\:log\:b+ \dfrac{2}{9}\:log\:c}}$

$\mathsf{\dfrac{9}{3}\:log\:a + \dfrac{1}{3}\:log\:b - \dfrac{14}{9}\:log\:b - \dfrac{2}{9}\:log\:c }$

$\mathsf{3\:log\:a - \dfrac{11}{9}\:log\:b - \dfrac{2}{9}\:log\:c}$

$\mathsf{log\left(\dfrac{a^3}{\sqrt[9]{\mathsf{b^{11}.c^2}}}\right)}$