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

(4^(log_(4)(5sqrty)))
Answer:

Express the given expression without logs, in simplest form. Assume all variables represent positive values. $\newline$ $\left(4^{\log _{4}(5 \sqrt{y})}\right)$ $\newline$ Answer:

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Full solution

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

\newline

\left(4^{\log _{4}(5 \sqrt{y})}\right)

\newline

Answer:

Apply Property: We are given the expression $4^{\log_{4}(5\sqrt{y})}$ . To express this without logs, we use the property that $a^{\log_a(b)} = b$ , where $a$ is the base of the logarithm and $b$ is the argument of the logarithm.
Simplify Expression: Applying the property to our expression, we have: $\newline$ $4^{\log_{4}(5\sqrt{y})} = 5\sqrt{y}$ $\newline$ This is because the base of the logarithm ( $4$ ) and the base of the exponent ( $4$ ) are the same.
Final Result: Now, we simplify the expression $5\sqrt{y}$ . Since there are no further logarithms or exponents to simplify, this is already in its simplest form.

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