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

ln(e^(3w^(2)))
Answer:

Express the given expression without logs, in simplest form. Assume all variables represent positive values. $\newline$ $\ln \left(e^{3 w^{2}}\right)$ $\newline$ Answer:)

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Simplify radical expressions with variables

Full solution

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

\newline

\ln \left(e^{3 w^{2}}\right)

\newline

Answer:)

Apply logarithmic property: The given expression is $\ln(e^{3w^{2}})$ . To express this without logs, we need to use the property of logarithms that states $\ln(a^{b}) = b \cdot \ln(a)$ .
Use $\ln(e^x)$ property: Since the base of the natural logarithm $\ln$ is $e$ , and we have $\ln(e^{3w^{2}})$ , we can apply the property directly. The natural logarithm $\ln$ and the base $e$ are inverse functions, so $\ln(e^x) = x$ .
Apply property to expression: Applying this property to our expression, we get $\ln(e^{3w^{2}}) = 3w^{2}$ .
Final simplified form: There is no need to simplify further, as $3w^{2}$ is already in its simplest form.

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