Question

qual o logaritimo de log 0,25 32

Answer 1

Boa tarde!

Solução!

$log_{0,25}32\\\\\ Lembrando~~que:\\\\\ 0,25= \dfrac{25}{100}= \dfrac{1}{4}= \dfrac{1}{2^{2} }\\\\\ 32=2^{5}$


$log_{0,25}32\\\\\ log_{0,25}32=x\\\\\ ( 0,25)^{x}=32\\\\\\ \left ( \dfrac{1}{4} \right )^{x}=32\\\\\\ \left ( \dfrac{1}{2^{2} } \right )^{x}=2^{5} \\\\\\ Invertendo~~a~~frac\~ao~~o~~expoente~~fica~~negativo!\\\\\ (2^{-2})^{x}=2^{5} \\\\\\ 2^{-2x}=2^{5}$

$-2x=5\\\\\ x=- \dfrac{5}{2}$


$\boxed{Resposta:log_{0,25}32= -\frac{5}{2}}$



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Bons estudos!