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

(12^(log_(12)(10sqrtw)))
Answer:

Express the given expression without logs, in simplest form. Assume all variables represent positive values. $\newline$ $\left(12^{\log _{12}(10 \sqrt{w})}\right)$ $\newline$ 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(12^{\log _{12}(10 \sqrt{w})}\right)

\newline

Answer:

Given Expression: We are given the expression $12^{\log_{12}(10\sqrt{w})}$ . The property of logarithms that we will use is $a^{\log_a(b)} = b$ , where $a$ is the base of the logarithm and $b$ is the argument of the logarithm.
Apply Property of Logarithms: Apply the property of logarithms to the given expression. Since the base of the logarithm and the base of the exponent are the same $12$ , we can simplify the expression to the argument of the logarithm. $12^{\log_{12}(10\sqrt{w})} = 10\sqrt{w}$
Simplify Expression: Now we have the simplified expression without logs, which is $10\sqrt{w}$ . This is already in its simplest form, assuming $w$ is a positive value as stated in the problem.

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