Expand the Logarithmic Expression natural log of 12 root of e

Problem

ln(√(12,e))

Solution

1. Rewrite the radical expression using a fractional exponent. The 12 root of a value is equivalent to raising that value to the power of 1/12

ln(e(1/12))

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

1/12*ln(e)

3. Simplify the expression by evaluating the natural logarithm of e Since ln(e)=1 the expression simplifies further.

1/12⋅1

Final Answer

ln(√(12,e))=1/12

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