Use the properties of logarithms to simplify the expression by eliminating all exponents and radicals. Assume that \( x, y>0 \). \( \log \left(\frac{\sqrt[4]{x}}{y^{5}}\right)=\square \)

We start with the expression \[ \log \left(\frac{\sqrt[4]{x}}{y^{5}}\right) \] and first rewrite the radical as an exponent: \[ \sqrt[4]{x} = x^{\frac{1}{4}}. \] Thus, the expression becomes: \[ \log \left(\frac{x^{\frac{1}{4}}}{y^{5}}\right). \] Next, we use the quotient rule for logarithms: \[ \log \left(\frac{a}{b}\right) = \log a - \log b, \] which gives: \[ \log \left(\frac{x^{\frac{1}{4}}}{y^{5}}\right) = \log \left(x^{\frac{1}{4}}\right) - \log \left(y^{5}\right). \] Then, we apply the power rule for logarithms: \[ \log \left(a^b\right) = b \log a. \] So we obtain: \[ \log \left(x^{\frac{1}{4}}\right) = \frac{1}{4}\log (x) \] and \[ \log \left(y^{5}\right) = 5\log (y). \] Thus, the simplified expression is: \[ \frac{1}{4}\log (x) - 5\log (y). \]