Condense into a single logarithm. Do not use fractional or negative exponents in your answer. You can type sqrt [n](m) as root(n)(m). (1)/(4)log_(6)(x)-10log_(6)(y) square

To condense the given expression into a single logarithm, we can use the properties of logarithms.<br /><br />Given expression: $\frac{1}{4}\log_{6}(x) - 10\log_{6}(y)$<br /><br />Step 1: Apply the power rule of logarithms.<br />$\frac{1}{4}\log_{6}(x) - 10\log_{6}(y) = \log_{6}(x^{\frac{1}{4}}) - \log_{6}(y^{10})$<br /><br />Step 2: Apply the quotient rule of logarithms.<br />$\log_{6}(x^{\frac{1}{4}}) - \log_{6}(y^{10}) = \log_{6}\left(\frac{x^{\frac{1}{4}}}{y^{10}}\right)$<br /><br />Therefore, the condensed expression is:<br />$\log_{6}\left(\frac{x^{\frac{1}{4}}}{y^{10}}\right)$