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

log 5x^(2)
Answer:

Expand the logarithm fully using the properties of logs. Express the final answer in terms of $\log x$ . $\newline$ $\log 5 x^{2}$ $\newline$ 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 5 x^{2}

\newline

Answer:

Identify Properties: Identify the properties of logarithms to be used for expanding $\log 5x^{2}$ . The expression $5x^{2}$ is a product of $5$ and $x^{2}$ . To expand the logarithm, we will use the product property of logarithms, which states that the logarithm of a product is equal to the sum of the logarithms of the individual factors. Additionally, we will use the power property of logarithms, which states that the logarithm of a power is equal to the exponent times the logarithm of the base.
Apply Product Property: Apply the product property to expand $\log 5x^{2}$ . Using the product property, we can write $\log 5x^{2}$ as the sum of $\log 5$ and $\log x^{2}$ . $\log 5x^{2} = \log 5 + \log x^{2}$
Apply Power Property: Apply the power property to the term $\log x^{2}$ . $\newline$ Using the power property, we can move the exponent in $\log x^{2}$ to the front of the logarithm. $\newline$ $\log x^{2} = 2 \times \log x$
Substitute Expanded Log: Substitute the expanded log $x^{2}$ back into the equation from Step $2$ . $\newline$ Now we replace $\log x^{2}$ with $2 \cdot \log x$ in the equation we obtained in Step $2$ . $\newline$ $\log 5x^{2} = \log 5 + 2 \cdot \log x$

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