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

log_(6)(6^(8w^(2)))
Answer:

Express the given expression without logs, in simplest form. Assume all variables represent positive values. $\newline$ $\log _{6}\left(6^{8 w^{2}}\right)$ $\newline$ 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 _{6}\left(6^{8 w^{2}}\right)

\newline

Answer:

Identify Property: Identify the property of logarithms that allows us to simplify $\log_{6}(6^{8w^{2}})$ . The property that we will use is the inverse property of logarithms, which states that $\log_{b}(b^{x}) = x$ for any base $b$ and exponent $x$ .
Apply Property: Apply the inverse property of logarithms to simplify the expression. $\newline$ Since the base of the logarithm and the base of the exponent are the same (both are $6$ ), we can apply the inverse property directly. $\newline$ $\log_{6}(6^{8w^{2}}) = 8w^{2}$

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