Questions: Simplify the expression without using a calculator. ln(1/e^5)=

Simplify the expression without using a calculator. ln(1/e^5)=
Transcript text: Simplify the expression without using a calculator. \[ \ln \left(\frac{1}{e^{5}}\right)= \]
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Solution

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Solution Steps

Step 1: Rewrite the expression

We can rewrite 1/e⁵ as e⁻⁵. So the expression becomes ln(e⁻⁵).

Step 2: Use the property of logarithms

Recall that logₐ(aˣ) = x. In our case, the base of the natural logarithm (ln) is _e_. Therefore, ln(e⁻⁵) simplifies to -5.

Final Answer:

The simplified expression is -5.

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