Condense the expression to a single logarithm using the properties of logarithms. \[ \log (x)-\frac{1}{2} \log (y)+6 \log (z) \] Enclose arguments of functions in parentheses and include a multiplication sign betw example, \( c^{*} \log (h) \).

To condense the expression \( \log (x) - \frac{1}{2} \log (y) + 6 \log (z) \), we can use the properties of logarithms. First, we rewrite \( -\frac{1}{2} \log (y) \) as \( \log (y^{-\frac{1}{2}}) \), which can also be written as \( \log \left(\frac{1}{\sqrt{y}}\right) \). Next, we rewrite \( 6 \log (z) \) as \( \log (z^{6}) \). Now, we combine these terms: \[ \log(x) + \log(z^{6}) - \log(y^{\frac{1}{2}}) = \log\left(x \cdot z^{6}\right) - \log\left(y^{\frac{1}{2}}\right) \] Using the property that \( \log(a) - \log(b) = \log\left(\frac{a}{b}\right) \), we can write: \[ \log\left(\frac{x \cdot z^{6}}{y^{\frac{1}{2}}}\right) \] Thus, the condensed expression is: \[ \log\left(\frac{x \cdot z^{6}}{y^{*} \sqrt{y}}\right) \]