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Express the given expression without logs, in simplest form. Assume all variables represent positive values.

log_(7)(7^(w^(2)))
Answer:

Express the given expression without logs, in simplest form. Assume all variables represent positive values. $\newline$ $\log _{7}\left(7^{w^{2}}\right)$ $\newline$ Answer:

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Product property of logarithms

Full solution

Q. Express the given expression without logs, in simplest form. Assume all variables represent positive values.

\newline

\log _{7}\left(7^{w^{2}}\right)

\newline

Answer:

Recognize Property: Recognize the logarithmic property that allows simplification of the expression $\log_{7}(7^{w^{2}})$ . The property states that $\log_{b}(b^{x}) = x$ for any base $b$ and exponent $x$ .
Apply Property: Apply the logarithmic property to the given expression. $\newline$ Since the base of the logarithm and the base of the exponent are the same $7$ , we can simplify the expression to just the exponent. $\newline$ Therefore, $\log_{7}(7^{w^{2}}) = w^2$ .

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