Value of ln(e^2) | Simplify Natural log of e^2

The natural log of e^2 is denoted by ln(e²) and its value is equal to 2. That is, the value of ln(e^2) is given by

ln(e²) = 2.

ln(e²) Formula

As ln(e^k) = k, the formula of ln(e²) is given as follows:

$\boxed{\ln e^k = k}$

Proof of ln(e²) = 2

Let us assume that

x = ln(e²).

As ln = log_e, this implies that

x = log_e e².

⇒ x =2 log_ee using the logarithm rule log_ab^k = k log_ab.

⇒ x =2 × 1 as we know log_aa = 1.

⇒ x =2.

Therefore, the value of ln(e²) is equal to 2.

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