Question

BOM DIAAA!!!

Calcule os seguintes logs:
a) $log_{9} \sqrt[5]{81}$

b) $log _{3} (log _{x} 27)=1$

c)$log _{2} 16 - log_{4} 32$

Answer 1

Oi Carol, (liberdade)!

use as propriedades, da definição, decorrente da definição e da potência:

$\boxed{log_bc=a~\to~c=b^a}\\\\ \boxed{log(b)^n~\to~n\cdot logb}\\\\ \boxed{log_bb=1}$

vamos lá..

$log_9 \sqrt[5]{81}=x\\ 9^x= \sqrt[5]{9^2}\\ \not9^x=\not9^{ \tfrac{2}{5} }\\\\ \large\boxed{\boxed{x= \dfrac{2}{5}}}$

______________

$log_3(log_x27)=1\\ log_x27=3^1\\ log_x27=3\\ x^3=27\\ x= \sqrt[3]{27}\\ x= \sqrt[3]{3^3}\\\\ \large\boxed{\boxed{x=3}}$

______________

$log_216-log_432=log_2(2^4)-log_4(2^5)\\ log_216-log_432=4\cdot log_22-log_{2^2}(2^5)\\ log_216-log_432=4\cdot log_22-log_2(2^{ \tfrac{5}{2} })\\\\ log_216-log_432=4\cdot1- \dfrac{5}{2}\cdot1\\\\ log_216-log_432=4- \dfrac{5}{2}\\\\ \Large\boxed{\boxed{log_216-log_432= \dfrac{3}{2}}}$

Tenha ótimos estudos ;D