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))/(sqrtzy^(2))) 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))/(sqrtzy^(2))) Answer:

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Apply Quotient Rule: Apply the quotient rule of logarithms to the expression log((x^(2))/(sqrt(y)*y^(2))). Quotient rule of logarithms: log(a/b) = log(a) - log(b) log((x^(2))/(sqrt(y)*y^(2))) = log(x^(2)) - log(sqrt(y)*y^(2))Apply Product Rule: Apply the product rule of logarithms to the denominator part of the expression log(sqrt(y)*y^(2)). Product rule of logarithms: log(a*b) = log(a) + log(b) log(sqrt(y)*y^(2)) = log(sqrt(y)) + log(y^(2))Apply Power Rule: Apply the power rule of logarithms to the expressions log(x^(2)), log(sqrt(y)), and log(y^(2)). Power rule of logarithms: log(a^n) = n*log(a) log(x^(2)) = 2*log(x) log(sqrt(y)) = log(y^(1/2)) = (1/2)*log(y) log(y^(2)) = 2*log(y)Substitute Results: Substitute the results from Step 3 into the expression from Step 1. log((x^(2))/(sqrt(y)*y^(2))) = 2*log(x) - ((1/2)*log(y) + 2*log(y))Distribute and Combine: Distribute the negative sign and combine the logarithmic terms involving log(y). 2*log(x) - (1/2)*log(y) - 2*log(y) = 2*log(x) - (1/2 + 2)*log(y)Simplify Expression: Simplify the expression by combining the coefficients for log(y). 2*log(x) - (1/2 + 2)*log(y) = 2*log(x) - (5/2)*log(y)Write Final Form: Write the final expanded form of the logarithm. The final expanded form is 2*log(x) - (5/2)*log(y).

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

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