Question

Ajudeem!!   
Logarítimos
  (A) log5 (5a/bc)  
  (B) log3 (a* b^3/c * raiz cubica de a²)

Answer 1

Propriedades:

$log _{n}(xy)\to~log _{n}x*log _{n}y~\to~log _{n}x+log _{n}y~~(LOG~DO~PRODUTO)\\\\ log _{n}( \frac{x}{y})\to~log _{n}x/log _{n}y~\to~log _{n}x-log _{n}y~(LOG~DO~QUOCIENTE)\\\\ logx ^{n}~\to~n*log~~(LOG~DA~POTENCIA)\\\\ log _{x}y=n~\to~x ^{n}=y$


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$log _{5}( \frac{5a}{bc})=log _{5} 5a-log _{5}bc\\\\ log _{5}( \frac{5a}{bc})=(log _{5}5*log _{5}a)-log _{5}b*log _{5}c\\\\ log _{5}( \frac{5a}{bc})=(log _{5}5+log _{5}a)-log _{5}b+log _{5}c\\\\ \boxed{log _{5}( \frac{5a}{b})=(1+log _{5}a)-log _{5}b+log _{5}c}$

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$log _{3}( \frac{ab ^{3} }{c \sqrt[3]{a ^{2} } })=log _{3}(ab ^{3})-log _{3}c \sqrt[3]{a ^{2} }\\\\ log _{3}( \frac{ab ^{3} }{ c\sqrt[3]{a ^{2} } })=(log _{3}a*log _{3}b ^{3})-log _{3}(c*a ^{ \frac{2}{3} })\\\\ log _{3}( \frac{ab ^{3} }{c \sqrt[3]{a ^{2} } })=(log _{3}a+3*log_{3}b)-log _{3}c*log_{3}a ^{ \frac{2}{3} }\\\\ log _{3}( \frac{ab ^{3} }{c \sqrt[3]{a ^{2} } })=(log _{3}a+3log _{3}b)-log _{3}c+ \frac{2}{3}*log _{3}a$

$log _{3}( \frac{ab ^{3} }{c \sqrt[3]{a ^{2} } })=(log _{3}a+3log _{3}b)-log _{3}c+ \frac{2}{3}log _{3}a\\\\ log _{3}( \frac{ab ^{3} }{c \sqrt[3]{a ^{2} } })= (\frac{2}{3}log _{3}a+log _{3}a+3log _{3}b)-log _{3}c\\\\ \boxed{log _{3}( \frac{ab ^{3} }{c \sqrt[3]{a ^{2} } })=\frac{5}{3}log _{3}a+3log _{3}b-log _{3}c}$

Espero ter ajudado e tenha ótimos estudos xD