[tex]log_{2\sqrt{2}}\frac{1}{4}=log_{2\cdot2^{\frac{1}{2}}}2^{-2}=-log_{2^{\frac{3}{2}}}2=-\frac{log2^2}{log2^{\frac{3}{2}}}}=-\frac{2log2}{{\frac{3}{2}log2}}=-\frac{4}{3}[/tex]
