Expand the logarithm fully using the properties of logs. Express the final answer in terms of log x,log y, and log z. log ((y^(2)root(3)(z^(2)))/(x^(5))) 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 ((y^(2)root(3)(z^(2)))/(x^(5))) 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 are relevant here are the quotient property, the power property, and the property for the logarithm of a root. Quotient Property: log_b(P/Q) = log_b(P) - log_b(Q) Power Property: log_b(P^k) = k * log_b(P) Root Property: log_b(root(k)(P)) = (1/k) * log_b(P)Apply Quotient Property: Apply the quotient property to the given logarithm. The given logarithm is of the form log((y^(2) * root(3)(z^(2)))/(x^(5))). According to the quotient property, this can be written as: log(y^(2) * root(3)(z^(2))) - log(x^(5))Apply Power Property: Apply the power property to the terms with exponents. The term log(y^(2)) can be expanded using the power property as: 2 * log(y) Similarly, the term log(x^(5)) can be expanded as: 5 * log(x)Apply Root Property: Apply the root property to the term with the cube root. The term root(3)(z^(2)) can be written as z^(2/3), and applying the power property to log(z^(2/3)) gives us: (2/3) * log(z)Combine Results: Combine the results from the previous steps to write the final expanded form. The expanded form of the given logarithm is: 2 * log(y) + (2/3) * log(z) - 5 * log(x)

Expand the logarithm fully using the properties of logs. Express the final answer in terms of $\log x, \log y$ , and $\log z$ . $\newline$ $\log \frac{y^{2} \sqrt[3]{z^{2}}}{x^{5}}$ $\newline$ Answer:

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