a) log_{\frac{1}{4}}\sqrt2=x\\ (\frac{1}{4})^x=\sqrt2\\ (\frac{1}{2})^{2x}=2^{\frac{1}{2}}\\(\frac{1}{2})^{2x}=(\frac{1}{2})^{-\frac{1}{2}}\\ 2x=-\frac{1}{2}|:2 \\ x=-\frac{1}{4}
log_{\frac{1}{4}}\sqrt2=-\frac{1}{4}
b)
log_{\frac{1}{5}}5\sqrt5=x\\ (\frac{1}{5})^x=5\sqrt5\\ (\frac{1}{5})^x=5^1\cdot 5^{\frac{1}{2}}\\ (\frac{1}{5})^x=5^{1\frac{1}{2}}\\ (\frac{1}{5})^x=(\frac{1}{5})^{-1\frac{1}{2}}\\ x=-1\frac{1}{2}\\x=-1,5\\ log_{\frac{1}{5}}5\sqrt5=-1,5