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

log_(6)(6^(3z^(3)))
Answer:

Express the given expression without logs, in simplest form. Assume all variables represent positive values. $\newline$ $\log _{6}\left(6^{3 z^{3}}\right)$ $\newline$ 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^{3 z^{3}}\right)

\newline

Answer:

Identify Property: Identify the property of logarithms that allows us to simplify $\log_{6}(6^{3z^{3}})$ . 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 to directly find the exponent. $\newline$ Therefore, $\log_{6}(6^{3z^{3}}) = 3z^{3}$ .

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