Once you remember the definition of a log, the answer to this question will literally fall out of your pencil.
First, ' Ln ' means 'natural log' ... logs to the base of ' e '.
Definition of the natural log of a number: In order to get the number, what power do I have to raise ' e ' to ?
OK. What power do you have to raise ' e ' to in order to get 1/e² ?
Isn't 1/e² the same thing as e⁻² ?
So, in order to get 1/e² , you have to raise ' e ' to the -2 power .
In math-speak: ** Ln(1/e²) = -2 ** .
Ln 1/e² = Ln 1 - Ln e² as Ln X/Y = Ln X - Ln Y = 0 - 2 Ln e as Ln 1 = 0 and Ln X² = 2 Ln X = - 2 * 1 as Ln e = 1
= -2
The natural logarithm of e 2 1 simplifies to -2. This is derived by using logarithmic properties including the properties of ln ( 1 ) and ln ( e n ) . Thus, ln ( e 2 1 ) = − 2 .
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