Natural Log Formula
Natural log of a number is the other of representing a number. Various natural log formulas are,
- ln (1) = 0
- ln (e) = 1
- ln (-x) = Not Defined {log of negative number is Not-Defined}
- ln (∞) = ∞
- ln(ex) = x, x ∈ R
Product Rule for Natural Log
When we have a natural log of the product of two numbers, then it can be represented as the addition of the natural log of the first number and the natural log of the second number.
ln(xy) = ln x + ln y
Quotient Rule for Natural Log
When we have a natural log of a fraction of two numbers, then it can be represented as the subtraction of natural log of the first number and the natural log of the second number.
ln(x/y) = ln x – ln y
Power Rule for Natural Log
When we have a natural log of x to power r, then it can be represented as r times ln x
ln(xr) = r.ln x
Reciprocal Rule for Natural Log
When we have a natural log of reciprocal of x, it can be represented as minus of the natural log of x.
ln(1/x) = -ln x
Change of Base for Natural Log
Base of log can be easily changed using the formula,
loge a = (logc a)/(logc e)
Natural Log Formulae Table |
|
---|---|
Representation of Natural Log | loge x = ln x |
ln (1) | ln 1 = 0 |
ln (e) | ln e = 1 |
ln (-x) | Not defined |
ln (∞) | ∞ |
Conversion Formula |
ln x = y ⇔ ey = x |
eln x | x , x>0 |
ln (ex) | x , x ∈ R |
Product Rule | ln(xy) = ln x + ln y |
Quotient Rule | ln(x/y) = ln x – ln y |
Power Rule | ln(xr) = r.ln x |
Reciprocal Rule | ln(1/x) = -ln x |
Base change Rule | logba = (ln a)/(ln b) |
Equality of ln | ln x = ln y ⇔ x = y |
Natural Log
Natural Log in mathematics is a way of representing the exponents. We know that a logarithm is always defined with abase and for the natural log, the base is “e”. The natural log is used for solving various problems of Integration, Differentiation, and others.
In this article, we will learn about Natural log, Natural Log Formula, Examples, and others in detail.
Table of Content
- What is Natural Log?
- Natural Log Formula
- Natural Logarithms Table
- Natural Log Derivatrive
- Natural Log Integration
- Natural Lag Laws