Pré-Vestibular

Rodrigues

Sabendo que $\log x$ = 8, então o valor da expressão $\sqrt{\frac{x^3\sqrt{x}}{\sqrt[3]{x}\cdot\sqrt[4]{x}}}$ será:

a) $\frac{35}{2}$

b) $\frac{35}{3}$

c) $\frac{35}{4}$

d) $\frac{-35}{3}$

e) $35$

Resposta

Resposta: Letra B

$\log\sqrt{\frac{x^3\sqrt{x}}{\sqrt[3]{x}\cdot\sqrt[4]{x}}}=$
$\log\sqrt{\frac{x^3\cdot x^\frac{1}{2}}{x^\frac{1}{3}\cdot x^\frac{1}{4}}}=$
$\log\sqrt{\frac{x^{3+\frac{1}{2}}}{x^{\frac{1}{3}+\frac{1}{4}}}=$
$\log\sqrt{\frac{x^\frac{7}{2}}{x^\frac{7}{12}}=$
$=\log\sqrt{x^{\frac{7}{2}-\frac{7}{12}}}=$
$=\log\sqrt{x^{\frac{35}{12}}}=$
$=\log (x^{\frac{35}{12}})^\frac{1}{2}=$
$=\log x^{\frac{35}{12}\cdot\frac{1}{2}}=$
$=\log x^{\frac{35}{24}}=$
$=\frac{35}{24}\cdot\log x=$
$=\frac{35}{24}\cdot8=$
$=\frac{35}{3}$

Pré-Vestibular ⇒ (UFPB) Logaritmo Tópico resolvido

(UFPB) Logaritmo

Re: (UFPB) Logaritmo

Pré-Vestibular ⇒ (UFPB) Logaritmo Tópico resolvido

(UFPB) Logaritmo

Re: (UFPB) Logaritmo

Entrar • Registrar