Expand the logarithm fully using the properties of logs. Express the final answer in terms of log x,log y, and log z. log ((sqrtyz^(4))/(x^(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 ((sqrtyz^(4))/(x^(2))) Answer:

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Apply Quotient Rule: Let's start by applying the quotient rule of logarithms, which states that log(a/b) = log(a) - log(b). So, we have log((√(yz^(4)))/(x^(2))) = log(√(yz^(4))) - log(x^(2)).Deal with First Term: Now, let's deal with the first term, log(√(yz^(4))). The square root is the same as raising to the power of 1/2, so we can rewrite this as log((yz^(4))^(1/2)). Using the power rule of logarithms, which states that log(a^(n)) = n*log(a), we get log((yz^(4))^(1/2)) = (1/2)*log(yz^(4)).Apply Product Rule: Next, we apply the product rule of logarithms to the term log(yz^(4)), which states that log(ab) = log(a) + log(b). This gives us (1/2)*(log(y) + log(z^(4))).Apply Power Rule: Now, let's apply the power rule again to log(z^(4)), which gives us log(z^(4)) = 4*log(z). So, we have (1/2)*(log(y) + 4*log(z)).Distribute Coefficients: We can distribute the 1/2 to both terms inside the parenthesis, resulting in (1/2)*log(y) + (1/2)*4*log(z), which simplifies to (1/2)*log(y) + 2*log(z).Address Second Term: Now, let's address the second term from step 1, log(x^(2)). Applying the power rule of logarithms, we get log(x^(2)) = 2*log(x).Combine All Terms: Finally, we combine all the terms together to get the expanded form of the original logarithm. We have log(√(yz^(4))) - log(x^(2)) which becomes (1/2)*log(y) + 2*log(z) - 2*log(x).

Expand the logarithm fully using the properties of logs. Express the final answer in terms of $\log x, \log y$ , and $\log z$ . $\newline$ $\log \frac{\sqrt{y} z^{4}}{x^{2}}$ $\newline$ Answer:

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