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

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Final Answer: $\log (\frac{x^{4} y^{6}}{z^{20}})$

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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 $\log a + \log b = \log (a b)$ and $\log a - \log b = \log (\frac{a}{b})$ to combine the logs. This gives us $\log (\frac{x^{4} y^{6}}{(z^{2})^{10}})$ .

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

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

Condense the following expression by using the properties of logarithms.4log⁡x+6log⁡y−10log⁡z2

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