Question

Calcular $<var>log 1/4 \ 2 raiz 2</var>$

 

Answer 1

$<var>log_{\frac{1}{4} 2\sqrt2=x \Rightarrow(\frac{1}{4})^x=2\sqrt2\Rightarrow2^{-2x}=2^{\frac{3}{2}\Rightarrow-2x=\frac{3}{2}\Rightarrow x=-\frac{3}{4}</var>$

Answer 2

Olá, Luciana.

 

$<var>\log_{\frac14}2\sqrt2=\frac{\log_22\cdot2^{\frac12}}{\log_2\frac14}=\frac{\log_22^{\frac32}}{\log_22^{-2}}=\frac{\frac32\log_22}{-2\log_22}=\frac32 \cdot (-\frac12})=\boxed{-\frac34}</var>$