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

log_(8)(8^(2y^(2)))
Answer:

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

\newline

Answer:

Identify Property: Identify the property of logarithms that allows us to simplify $\log_{8}(8^{2y^{2}})$ . 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 Inverse 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 $8$ ), we can apply the inverse property directly. $\newline$ $\log_{8}(8^{2y^{2}}) = 2y^{2}$
Check for Simplifications: Check for any possible simplifications. The expression $2y^{2}$ is already in its simplest form, so no further simplifications are needed.

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