Natural Log Approximation

In mathematics, the natural logarithmic function approximation is defined as the function contains three ports, namely the number, the base and logarithm itself,  the natural logarithmic function approximation is the logarithm to the base of ‘e’ where e is constant, base of  ‘e’ value is given by

e = 2.718281828.

The natural logarithmic function approximation is represented as ln(x) or loge(x).

We take the value of base of ‘e’ is approximately e = 2.71.


Identities about natural log approximation:

For any positive values:

ln (x y) = ln(x) + ln (y)
ln (x/y) = ln (x) – ln (y)
ln (x^y) = y ln(x)
ln ex = x
eln (x) = x
log 1 = 1
e0 =1
ln (-ve) is not defined.


Some properties of natural log approximation:

1. Limx→0 ln (1+x)/x = 1

2. x/(1+x)`<=` ln(1+x) `<=` x for x`>` 1

3. ln (1) = 0

4. ln (-1) = i(`pi` )
Example Problems for Natural Log Approximation:

Problem 1:

To solve the natural logarithmic function of ln(8)

Solution:

Basic logarithmic function is ln(x`*` y) = ln(x) + ln (y)


Given function is   ln (8) = ln (4) + ln (4)

problem 2:

To solve natural logarithmic function of ln (7/3)

Solution:

Logarithmic function is ln(x/y) = ln(x) – ln(y)


Given function is   ln (7/3) = ln (7) – ln (3)

problem 3:

To solve natural logarithmic function of ln (23)

Solution:

Function is ln(xy) = y ln(x)

ln (23) = 3ln(2)

problem 4:

To solve the natural logarithmic function of in e10

Solution:

The function is ln ex = x

ln e10 = 10

I am planning to write more post on math answers to problems and Rounded Rectangle. Keep checking my blog.

problem 5:

To solve the natural logarithmic function of e0

Solution: Function is e0 = 1

Practices problems for natural logarithmic function:

Problem 1:

To solve the natural logarithmic of ln (9)

Solution:  ln (5) + ln (4)

Problem 2:

To solve natural logarithmic function of ln (12/5)

Solution: ln (12) – ln (5)

Problem 3:

To solve natural logarithmic function of ln(6^3)

Solution:  3ln (6)