Expand the logarithm fully using the properties of logs. Express the final answer in terms of log x,log y, and log z. log ((z^(4)root(3)(y))/(x)) 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 ((z^(4)root(3)(y))/(x)) Answer:

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Identify Properties: Identify the properties used to expand the logarithm. We will use the quotient property and the power property of logarithms to expand the given expression. Quotient Property: log_b (P/Q) = log_b P - log_b Q Power Property: log_b (P^k) = k * log_b PApply Quotient Property: Apply the quotient property to the given logarithm. Using the quotient property, we can separate the numerator and the denominator of the fraction inside the logarithm. log ((z^(4)root(3)(y))/(x)) = log (z^(4)root(3)(y)) - log (x)Apply Power Property (z^4): Apply the power property to the term z^(4) in the numerator. The term z^(4) can be expanded using the power property. log (z^(4)root(3)(y)) = 4 * log (z) + log (root(3)(y))Apply Power Property (root(3)(y)): Apply the power property to the term root(3)(y) in the numerator. The cube root of y is equivalent to y raised to the power of 1/3. log (root(3)(y)) = log (y^(1/3)) = (1/3) * log (y)Combine Results: Combine the results from steps 3 and 4. Now we combine the logarithms of z^(4) and root(3)(y) into a single expression. log (z^(4)root(3)(y)) = 4 * log (z) + (1/3) * log (y)Final Expanded Form: Combine all the results to get the final expanded form. Now we combine the results from steps 2, 3, 4, and 5 to get the final expanded form of the original logarithm. log ((z^(4)root(3)(y))/(x)) = 4 * log (z) + (1/3) * log (y) - log (x)

Expand the logarithm fully using the properties of logs. Express the final answer in terms of $\log x, \log y$ , and $\log z$ . $\newline$ $\log \frac{z^{4} \sqrt[3]{y}}{x}$ $\newline$ Answer:

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