Question

Me ajuda nesses 3 exercícios de logaritmos  que não conseguir fazer? 

 b)  $Log_{ 5} (0,000064)$ 

g) $Log_{9} (3 \sqrt{3} )$

h)  $Log_{2 } 0,25$

Answer 1

$a)log _{5}0,000064)=x\\\\ 5 ^{x}=0,000064\\\\ 5 ^{x}= \frac{1}{15.625}\\\\ 5 ^{x}= \frac{1}{5 ^{6} }\\\\ \not5 ^{x}=\not5 ^{-6}\\\\ \boxed{x=-6}$


$b)log _{9}(3 \sqrt{3})=x\\\\ 9 ^{x}=(3 \sqrt{3})\\\\ (3 ^{2}) ^{x}=( \sqrt{9*3})\\\\ 3 ^{2x}= (\sqrt{3 ^{2}* 3 ^{1} })\\\\ 3 ^{2x}=( \sqrt[2]{3 ^{3} })\\\\ \not3 ^{2x}=\not3 ^{ \frac{3}{2} }\\\\ 2x= \frac{3}{2}\\\\ \boxed{x= \frac{3}{4}}$


$log _{2}0,25=x\\\\ 2 ^{x}=0,25\\\\ 2 ^{x}= \frac{1}{4}\\\\ \not2 ^{x}=\not2 ^{-2} \\\\ \boxed{x=-2}$


Espero ter ajudado e tenha ótimos estudos ;D