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Expand the logarithm fully using the properties of logs. Express the final answer in terms of
log x.

log 6x^(4)
Answer:

Expand the logarithm fully using the properties of logs. Express the final answer in terms of $\log x$ . $\newline$ $\log 6 x^{4}$ $\newline$ Answer:

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Product property of logarithms

Full solution

Q. Expand the logarithm fully using the properties of logs. Express the final answer in terms of

\log x

.

\newline

\log 6 x^{4}

\newline

Answer:

Identify Properties: Identify the properties of logarithms to be used for expansion. $\newline$ The given logarithm is $\log 6x^{4}$ , which involves a product ( $6$ and $x^{4}$ ) and an exponent ( $4$ ). We will use the product property and the power property of logarithms to expand this expression.
Apply Product Property: Apply the product property of logarithms. $\newline$ The product property states that the logarithm of a product is equal to the sum of the logarithms of the individual factors. Therefore, we can write $\log 6x^{4}$ as $\log 6 + \log x^{4}$ .
Apply Power Property: Apply the power property of logarithms. $\newline$ The power property states that the logarithm of a number raised to an exponent is equal to the exponent times the logarithm of the number. Therefore, we can write $\log x^{4}$ as $4 \times \log x$ .
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ We have $\log 6 + \log x^{4}$ , which we can now rewrite using the power property as $\log 6 + 4 \cdot \log x$ .
Final Expanded Form: Since $\log 6$ is a constant, it cannot be simplified further. The final expanded form of the logarithm is $\log 6 + 4 \cdot \log x$ .

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