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What is the value of
ln root(3)(e^(2)) ?
Answer:

What is the value of $\ln \sqrt[3]{e^{2}}$ ? $\newline$ Answer:

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Relationship between squares and square roots

Full solution

Q. What is the value of

\ln \sqrt[3]{e^{2}}

?

\newline

Answer:

Rewrite cube root of $e^2$ : We are given the expression $\ln(\sqrt[3]{e^{2}})$ . The $\sqrt[3]{}$ indicates a cube root. We can rewrite the cube root of $e^2$ as $(e^2)^{\frac{1}{3}}$ .
Simplify using logarithm property: Using the property of logarithms that $\ln(a^b) = b\cdot\ln(a)$ , we can simplify the expression to $(\frac{1}{3})\cdot\ln(e^2)$ .
Further simplify expression: Since $\ln(e)$ is equal to $1$ , we can further simplify the expression to $(\frac{1}{3})\cdot 2\cdot \ln(e)$ .
Multiply to get final expression: Now, we multiply $2$ by $\frac{1}{3}$ to get $(\frac{2}{3})\cdot\ln(e)$ .
Final answer: Finally, since $\ln(e)$ equals $1$ , we multiply $\frac{2}{3}$ by $1$ to get the final answer.

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