Question

log de a×b³/c× raiz cúbica de a² na base 3, com cálculo por favor

Answer 1

Olá,

use as propriedades dfe logaritmos que você já estudou:

$\log_3\left( \dfrac{ab^3}{c \sqrt[3]{a^2} }\right)=\log_3(ab^3)-\log_3(c \sqrt[3]{a^2})\\\\ \log_3\left( \dfrac{ab^3}{c \sqrt[3]{a^2} }\right)=\log_3(a)+\log_3(b)^3-\log_3(c)+\log_3(a)^{ \tfrac{2}{3} }\\\\ \log_3\left( \dfrac{ab^3}{c \sqrt[3]{a^2} }\right)=\log_3(a)+3\cdot\log_3(b)-\left\log_3(c)+ \dfrac{2}{3}\cdot\log_3(a)\right\\\\ \log_3\left( \dfrac{ab^3}{c \sqrt[3]{a^2} }\right)=\log_3(a)+3\log_3(b)-\log_3(c)+ \dfrac{2}{3}\log_3(a)$

$\Large\boxed{\log_3\left( \dfrac{ab^3}{c \sqrt[3]{a^2} }\right)= \dfrac{5}{3}\log_3(a)+3\log_3(b)-\log_3(c)}$

Tenha ótimos estudos ;P