Expand the logarithm fully using the properties of logs. Express the final answer in terms of log x,log y, and log z. log ((x^(2)root(3)(y))/(z)) Answer:

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Expand the logarithm fully using the properties of logs. Express the final answer in terms of  log x,log y, and  log z.  log ((x^(2)root(3)(y))/(z)) Answer:

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Identify Properties: Identify the properties of logarithms that will be used to expand the given logarithm. The properties of logarithms that we will use are the quotient property, the power property, and the property for the logarithm of a root.Apply Quotient Property: Apply the quotient property to the given logarithm. The quotient property states that log_b(P/Q) = log_b(P) - log_b(Q). Therefore, we can write log((x^(2)root(3)(y))/z) as log(x^(2)root(3)(y)) - log(z).Apply Power Property: Apply the power property to the term log(x^(2)root(3)(y)). The power property states that log_b(P^k) = k*log_b(P). We can apply this to the term x^2 to get 2*log(x) + log(root(3)(y)).Apply Root Property: Apply the property for the logarithm of a root to the term log(root(3)(y)). The property for the logarithm of a root states that log_b(root(k)(P)) = (1/k)*log_b(P). We can apply this to the term root(3)(y) to get (1/3)*log(y).Combine Results: Combine the results from the previous steps to get the final expanded form. We have 2*log(x) + (1/3)*log(y) - log(z) as the expanded form of the given logarithm.

Expand the logarithm fully using the properties of logs. Express the final answer in terms of $\log x, \log y$ , and $\log z$ . $\newline$ $\log \frac{x^{2} \sqrt[3]{y}}{z}$ $\newline$ Answer:

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