Question

Ajudeeeem!!!

a) log3(ab²/c)

b) log2(a²raiz quadrada de b/raiz quadrada de c)

Answer 1

$log _{3}( \frac{ab^{2} }{c})$

Aplicando a p1, propriedade do produto

$\boxed{log _{n}(xy)~\to~log _{n}x*log _{n}y~\to~log _{n}x+log _{n}y}$

Aplicando a p2, propriedade do quociente

$\boxed{log _{n} (\frac{x}{y})~\to~log _{n}x-log _{n}y}$

E a p3, propriedade da potência

$\boxed{logx ^{n}~\to~n*logx}$

__________________

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


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$log _{2}( \frac{a ^{2} \sqrt{b} }{ \sqrt{c} })=(log _{2}a ^{2}* \sqrt{b})-log _{2} \sqrt{c} \\\\ log _{2}( \frac{a ^{2} \sqrt{b} }{ \sqrt{c} })=(log _{2}a ^{2}*log _{2} \sqrt{b})-log _{2}c ^{ \frac{1}{2} }\\\\ log _{2}( \frac{a ^{2} \sqrt{b} }{ \sqrt{c} })=(2*log _{2}a+log _{2}b ^{ \frac{1}{2} })- \frac{1}{2}*log _{2}c\\\\ log _{2}( \frac{a ^{2} \sqrt{b} }{ \sqrt{c} })=(2log _{2}a+ \frac{1}{2}*log _{2}b)- \frac{1}{2}log _{2}c$

$\boxed{log _{2}( \frac{a ^{2} \sqrt{b} }{ \sqrt{c} })=2log _{2}a+ \frac{1}{2}log _{2}b- \frac{1}{2}log _{2}c}$


Espero ter ajudado e tenha ótimos estudos =)