Question

resolva usando as propriedade de logaritmo.

Answer 1

$\log((\sqrt[3]{\frac{a^4\sqrt{ab}}{b^2\sqrt[3]{bc}}})^2)\\\\2\log(\sqrt[3]{\frac{a^4\sqrt{ab}}{b^2\sqrt[3]{bc}}})\\\\2[\log(\sqrt[3]{a^4\sqrt{ab}})-\log(\sqrt[3]{b^2\sqrt[3]{bc}})]$

$2[\log(\sqrt[3]{a^4.(ab)^{\frac{1}{2}}})-\log(\sqrt[3]{b^2(bc)^{\frac{1}{3}}}]\\\\2[\log(\sqrt[3]{a^{\frac{9}{2}}.b^{\frac{1}{2}}})-\log(\sqrt[3]{b^{\frac{7}{3}}.c^{\frac{1}{3}}})]\\\\2[\log({a^{\frac{9}{2}}.b^{\frac{1}{2}})^{\frac{1}{3}}-\log({b^{\frac{7}{3}}.c^{\frac{1}{3}})^{\frac{1}{3}}]$

$2[\frac{1}{3}\log({a^{\frac{9}{2}}.b^{\frac{1}{2}})-\frac{1}{3}\log({b^{\frac{7}{3}}.c^{\frac{1}{3}})]$

$2\{[\frac{1}{3}](\log({a^{\frac{9}{2}}.b^{\frac{1}{2}})-\log({b^{\frac{7}{3}}.c^{\frac{1}{3}}))\}$

$\frac{2}{3}[(\log({a^{\frac{9}{2}}.b^{\frac{1}{2}})-\log({b^{\frac{7}{3}}.c^{\frac{1}{3}})]$

$\frac{2}{3}\{[\log({a^{\frac{9}{2}})+\log(b^{\frac{1}{2}})]-[\log({b^{\frac{7}{3}})+(\log(c^{\frac{1}{3}})]\}$

$\frac{2}{3}(\frac{9}{2}\log a+\frac{1}{2}\log b-\frac{7}{3}\log b-\frac{1}{3}\log c)$

$\frac{2}{3}(\frac{27\log a+3\log b-14\log b-2\log c}{6})$

$\frac{27\log a-11\log b- 2\log c}{9}$