Question

alguém sabe fazer este logaritmo Paso a Paso
$log_{0.25}(2 \times \sqrt{2} ) = x$
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Answer 1

Explicação passo-a-passo:

Equação Logaritmica:

$\mathsf{\log_{0,25}\Big(2\sqrt{2}\Big)=x }$

$\mathsf{\log_{\Big(\frac{1}{4}\Big)}\sqrt{2^2.2}=x }$

$\mathsf{\log_{\Big(\frac{1}{4}\Big)}\sqrt{8}=x }$

Aplicando a definição dos logaritmos ter-se-á:

$\mathsf{\Big(\frac{1}{4}\Big)^x = \sqrt{8} }$

$\mathsf{\Big(\frac{1^2}{2^2}\Big)^x= 8^{\frac{1}{2}} }$

$\mathsf{\Big(\frac{1}{2}\Big)^{2x} = \Big(2^3\Big)^{\frac{1}{2}} }$

$\mathsf{\cancel{2}^{-2x}=\cancel{2}^{\frac{3}{2}} }$

$\mathsf{-2x=\frac{3}{2} }$

$\mathsf{x=\frac{3}{2}.-\frac{1}{2} }$

$\boxed{\boxed{\mathsf{x=-\frac{3}{4}}}}}$$\checkmark$

Espero ter ajudado bastante!)