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

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Identify Properties: Identify the properties used to expand log((xz^(2))/(y)). We will use the quotient property and the product property of logarithms to expand the given expression. Quotient Property: log_b (P/Q) = log_b P - log_b Q Product Property: log_b (PQ) = 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((xz^(2))/(y)) = log(xz^(2)) - log(y)Apply Product Property: Apply the product property to the logarithm of the numerator. Now we will separate the x and z^(2) terms using the product property. log(xz^(2)) = log(x) + log(z^(2))Apply Power Property: Apply the power property to the logarithm of z^(2). We will now apply the power property to the log(z^(2)) term to bring down the exponent. log(z^(2)) = 2 * log(z)Combine Results: Combine the results from Steps 2, 3, and 4 to get the final expanded form. Substitute the expanded form of log(z^(2)) from Step 4 into the equation from Step 3, and then combine it with the result from Step 2. log((xz^(2))/(y)) = (log(x) + 2 * log(z)) - log(y)Simplify Expression: Simplify the expression to get the final answer. log((xz^(2))/(y)) = log(x) + 2 * log(z) - log(y)

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

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