Question

Calcule o valor do logaritmo.

log ³√16 na base 1\2

Answer 1

Olá ! 

Vamos aplicar algumas regrinhas de log e de expoentes ... 

Sabemos que: 

$\sqrt[3]{16} = \sqrt[3]{2^{4}} =\boxed{2^{ \frac{4}{3} }}$


Agora basta resolver ... 

$log_{ \frac{1}{2} }\ \ \sqrt[3]{16} =x\\\\\\ log_{ \frac{1}{2} }\ \ 2^{ \frac{4}{3} }=x\\\\\\ ( \frac{1}{2} )^{x}=2^{ \frac{4}{3} }\\\\\\(2)^{-x}=(2)^{ \frac{4}{3} }\\\\\\ -x= \frac{4}{3} \\\\\\ \boxed{x=-\ \frac{4}{3} }\\\\\\\\\ Ent\~ao\ :$

$\boxed{\boxed{log_{ \frac{1}{2} }\ \ \sqrt[3]{16} \ =-\ \frac{4}{3} }}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ok$