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Expand the logarithm. Assume all expressions exist and are well-defined. $\newline$ Write your answer as a sum or difference of common logarithms or multiples of common logarithms. The inside of each logarithm must be a distinct constant or variable. $\newline$ $\log(w^2)$ $\newline$ _____

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Power property of logarithms

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Q. Expand the logarithm. Assume all expressions exist and are well-defined.

\newline

Write your answer as a sum or difference of common logarithms or multiples of common logarithms. The inside of each logarithm must be a distinct constant or variable.

\newline

\log(w^2)

\newline

_____

Identify Property: Identify the logarithmic property that allows expansion of $\log(w^2)$ . $\newline$ The power property of logarithms states that $\log_b(m^n) = n \cdot \log_b(m)$ , which can be used to expand $\log(w^2)$ .
Apply Power Property: Apply the power property to expand $\log(w^2)$ . $\newline$ Using the power property: $\log(w^2) = 2 \cdot \log(w)$ . $\newline$ This step expands the logarithm by taking the exponent and multiplying it with the logarithm of the base.

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