Condense the following expression by using the properties of logarithms. \[ 4 \log x+6 \log y-10 \log z^{2} \]

Step 1 ：We are given the expression \(4 \log x+6 \log y-10 \log z^{2}\).

Step 2 ：We can use the properties of logarithms to simplify this expression.

Step 3 ：First, we use the property \(\log a^n = n \log a\) to rewrite the expression as \(\log x^{4} + \log y^{6} - \log (z^{2})^{10}\).

Step 4 ：Next, we use the properties \(\log a + \log b = \log (ab)\) and \(\log a - \log b = \log \left(\frac{a}{b}\right)\) to combine the logs. This gives us \(\log \left(\frac{x^{4} y^{6}}{(z^{2})^{10}}\right)\).

Step 5 ：Simplifying the denominator gives us \(\log \left(\frac{x^{4} y^{6}}{z^{20}}\right)\).

Step 6 ：Final Answer: \(\boxed{\log \left(\frac{x^{4} y^{6}}{z^{20}}\right)}\)