Problem

Simplify the following natural logarithm with the non-zero constant $a$. \[ \ln \left(e^{-1 / a}\right) \] Answer:

Solution

Step 1 :Given the natural logarithm \(\ln \left(e^{-1 / a}\right)\).

Step 2 :The natural logarithm and the exponential function are inverse functions. Therefore, the natural logarithm of an exponential function simplifies to the exponent of the exponential function.

Step 3 :In this case, the exponent is \(-1/a\).

Step 4 :So, the simplified form of the given natural logarithm is \(\boxed{-\frac{1}{a}}\).

From Solvely APP
Source: https://solvelyapp.com/problems/7967/

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