[tex]log_{0,25}\sqrt2=\frac{log\sqrt2}{log0,25}=\frac{log2^{\frac{1}{2}}}{log\frac{1}{4}}=\frac{\frac{1}{2}log2}{log2^{-2}}=\frac{\frac{1}{2}log2}{-2log2}=\frac{\frac{1}{2}}{-2}=\frac{1}{2}\cdot(-\frac{1}{2})=-\frac{1}{4}[/tex]
