Solve for x natural log of 1/x=-5

Problem

ln(1/x)=−5

Solution

1. Apply the property of logarithms to rewrite the fraction inside the natural log using a negative exponent.

ln(x^(−1))=−5

2. Use the power rule for logarithms, ln(a^b)=b*ln(a) to move the exponent to the front.

−1⋅ln(x)=−5

3. Divide both sides by −1 to isolate the natural log term.

ln(x)=5

4. Rewrite in exponential form by applying the base e to both sides to solve for x

x=e^5

Final Answer

ln(1/x)=−5⇒x=e^5

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