Why lne = 1

Why lne = 1

because
LNX is the logarithm of X with E as the base
therefore
When x = e, e is the base, and the logarithm of E is 1

In mathematics, what are lne and ln1? 3Q

lne=1 ln1=0

What is [lne &;] / N equal to
Why n tends to infinity

Ah, although this problem may be definite integral
Because this expression can be written as log e (the nth power of E) / n
According to the logarithm formula, if the numerator of this fraction is n, then n / N = 1
If e is changed to x, this formula is the simplest and cannot be reduced

Given a > b, b > 0, prove the 3 sides of a + 3 sides of b > = 2 sides of a + 2 sides of a * B

Simple calculation of 1999 × 19981.998-1998 × 19991.999

1999×19981.998-1998×19991.999
=1999×1998×10.001-1998×1999×10.001
=0

This pile of sand weighs 24 tons in total. If 0.5 tons are transported from the first pile and the second pile to the third pile, the mass ratio of the three piles of sand is 2:1:3. How many tons are there in each pile?

Given 3 ^ a = 8,3 ^ B + 10, then the value of 3 ^ 3a-2b

3^(3a-2b) = (3^3a)/(3^2b)
= (3^a)^3/(3^b)^2
= 8^3/10^2
=51.2

Given that w = Z + I (Z belongs to c) and Z-2 / Z + 2 is a pure imaginary number, find the maximum of M = / W + 1 / ^ 2 + / W-1 / ^ 2 and the maximum of M is w

Let 2 correspond to a point on the complex plane, - 2 correspond to B, Z correspond to Z point
Then Z-2 / Z + 2 is a pure imaginary number if and only if the angle AZB is a right angle (the difference between the radiation angles of Z-2 and Z + 2)
So Z is on the circle with ab as the diameter, that is, | Z | = 2, then, | w-i | = 2
M = | W + 1 | ^ 2 + | W-1 | ^ 2 = (W + 1) (conjugate + 1 of W) + (W-1) (conjugate-1 of W) = 2 (| w | ^ 2 + 1)
|W | denotes the distance from point w to the origin, and the trajectory of W is a circle with I as the center and 2 as the radius, and its maximum distance to the origin is 3
That is, the maximum value of | w | is 3, then the maximum value of M is 20, and w = 3I

Banana, apple and pear are three kinds of fruits from the fruit shop, of which banana accounts for 20%. The ratio of pear quality to the sum of the other two kinds of fruits is 1:2, and the ratio of apples is 1:2
The banana weighs 40 kg, and the fruit shop has transported () kg of apples

Apples account for the total: (1-20% - 1 / 3) = 7 / 15 (the ratio of pear to the sum of the other two fruits is 1:2, so pears account for 1 / 3 of the total)
Imported apples: 40 / (7 / 15-20%) = 40 / 1 / 15 = 600 kg

If M is used to represent the number of fractions in the five real numbers of 3.14, - 35,27,2 π, - 6.31, then the value of M is ()
A. 2B. 3C. 4D. 5

Among the five real numbers 3.14, - 35, 27, 2 π, - 6.31, there are four fractions, namely 3.14, - 35, 27, - 6.31, M = 4