Why is lne equal to 1? How can it not be pressed on the scientific calculator?

Why is lne equal to 1? How can it not be pressed on the scientific calculator?

It's easy to understand that LNX is the logarithm of X with E as the base
When x = e, e is the base, and the logarithm of E is 1
If you don't understand it here, you can convert it into exponential form, that is, y = lne is converted into y power of e equal to e (E in the front is the base, and E in the back is the true number in the logarithmic function). Then you can see that y must be 1, which is what we often say: "the logarithm of the base is 1."
There's no e in the calculator?

Why is the limit (n - > positive infinity) of Ln (1 + 1 / N) ^ n equal to lne

From the second important limit, we know that:
When n - > ∞, LIM (1 + 1 / N) ^ n = E
So when n - > ∞, LIM (LN (1 + 1 / N) ^ n) = ln E

Is ln (1 + x ^ 2) equal to ln1 + LNX ^ 2?

Not wait
Of course, we have:
ln a+ln b=ln a*b
For your special case: ln 1 + ln x ^ 2 = ln 1 * x ^ 2 = ln x ^ 2