Evaluate 2 natural log of cube root of e

Problem

2*ln(√(3,e))

Solution

1. Translate the expression into mathematical notation using the properties of natural logarithms and radicals.

2*ln(e(1/3))

2. Apply the power rule for logarithms, which states that ln(ab)=b*ln(a)

2⋅1/3*ln(e)

3. Simplify the constant coefficients by multiplying them together.

2/3*ln(e)

4. Evaluate the natural logarithm of e knowing that ln(e)=1

2/3⋅1

5. Finalize the calculation to find the numerical value.

2/3

Final Answer

2*ln(√(3,e))=2/3

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