Question

preciso da ajuda de vocês?

Answer 1

Olá Aninha,

use as seguintes propriedades:

$log _{n} ab~\to~log _{n}a+log _{n}b$

$log _{n} \frac{a}{b}~\to~log _{n}a-log _{n}b$

$logb ^{c}~\to~c*logb$

$log _{b}c=a~\to~b ^{a}=c$

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$log _{16} \sqrt[3]{4}=x\\ 16 ^{x}= \sqrt[3]{4}\\ (4 ^{2}) ^{x}=4 ^{ \frac{1}{3} }\\ 4 ^{2x}=4 ^{ \frac{1}{3} }\\ \not4 ^{2x}=\not4 ^{ \frac{1}{3} } \\ 2x= \frac{1}{3}\\\\ \boxed{x= \frac{1}{6}}$

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$log1000=x\\ log _{10}1000=x\\ log_{10}10 ^{3}=x\\ x=3*log10\\ x=3*1\\ \boxed{x=3}$

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$log _{13} \frac{45}{10}=log _{13}45-log _{13}10\\\\ log _{13} \frac{45}{10}=(log _{13}9*5)-(log _{13}2*5)\\\\ log _{13} \frac{45}{10}=(log _{13}9+log _{13}5)-(log _{13}2+log _{13}5)\\\\ log _{13} \frac{45}{10}=(1,2+1,6)-(3,7+1,6)\\\\ log _{13} \frac{45}{10}=2,8-5,3\\\\ \boxed{log _{13} \frac{45}{10}=-2,5}$


Espero ter ajudado e tenha ótimos estudos =))