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

(4^(log_(4)(4sqrtz)))
Answer:

Express the given expression without logs, in simplest form. Assume all variables represent positive values. $\newline$ $\left(4^{\log _{4}(4 \sqrt{z})}\right)$ $\newline$ 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

\left(4^{\log _{4}(4 \sqrt{z})}\right)

\newline

Answer:

Recognize Property of Logarithms: Recognize the property of logarithms that allows us to simplify the expression. $\newline$ The expression is $4^{\log_{4}(4\sqrt{z})}$ . According to the property of logarithms, $a^{\log_{a}(b)} = b$ , where a > 0 and $a \neq 1$ .
Apply Property: Apply the property to the given expression. $\newline$ Using the property from Step $1$ , we can simplify $4^{\log_{4}(4\sqrt{z})}$ to just $4\sqrt{z}$ because the base of the logarithm and the base of the exponent are the same.
Check for Simplifications: Check for any further simplifications. Since $4\sqrt{z}$ is already in its simplest form and there are no further logarithmic operations to perform, we conclude that this is the final answer.

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