Answer :
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
= 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
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 .
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 .
