Solve for x natural log of 1/e=x

Problem

ln(1/e)=x

Solution

1. Rewrite the fraction inside the natural logarithm using the property of negative exponents, where 1/(a^n)=a^(−n)

1/e=e^(−1)

2. Substitute this expression back into the original equation.

ln(e^(−1))=x

3. Apply the inverse property of logarithms, which states that ln(e^a)=a for any real number a

−1=x

4. Identify the value of x from the resulting equation.

x=−1

Final Answer

ln(1/e)=−1

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