X

ln meaning in Maths ?

( 5 )  .  1 Rating
1238 views   .  0 comments  .   . 

Download Solution PDF

Answer: What is Natural Log mean?

The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718281828459. The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x. Parentheses are sometimes added for clarity, giving ln(x), loge(x), or log(x). This is done particularly when the argument to the logarithm is not a single symbol, so as to prevent ambiguity.

The natural logarithm of x is the power to which e would have to be raised to equal x. For example, ln 7.5 is 2.0149..., because e2.0149... = 7.5. The natural logarithm of e itself, ln e, is 1, because e1 = e, while the natural logarithm of 1 is 0, since e0 = 1.

The natural logarithm can be defined for any positive real number a as the area under the curve y = 1/x from 1 to a (with the area being negative when 0 < a < 1). The simplicity of this definition, which is matched in many other formulas involving the natural logarithm, leads to the term "natural". The definition of the natural logarithm can then be extended to give logarithm values for negative numbers and for all non-zero complex numbers, although this leads to a multi-valued function: see Complex logarithm for more.

The natural logarithm function, if considered as a real-valued function of a real variable, is the inverse function of the exponential function, leading to the identities:

e ln ⁡ x = x if x is strictly positive , ln ⁡ e x = x if x is any real number . {\displaystyle {\begin{aligned}e^{\ln x}&=x\qquad {\text{ if }}x{\text{ is strictly positive }},\\\ln e^{x}&=x\qquad {\text{ if }}x{\text{ is any real number .}}\end{aligned}}}

Like all logarithms, the natural logarithm maps multiplication of positive numbers into addition:

ln ⁡ reference

Take Quiz To Earn Credits!

Turn Your Knowledge into Earnings.




Give Rating
Report
Write Your Comments or Explanations to Help Others
Comments(0)





Miscellaneous in Maths
Data Interpretation Questions in Maths
Number System Questions in Maths
Percentage Aptitude Questions in Maths
Profit and Loss Questions in Maths
Time and Work Questions in Maths
Geometry Questions and answer in Maths
Ratio and Proportion Questions in Maths
Compound interest questions in Maths
Volume and Surface Area Questions in Maths
Average Questions in Maths

Ever curious about what that abbreviation stands for? fullforms has got them all listed out for you to explore. Simply,Choose a subject/topic and get started on a self-paced learning journey in a world of fullforms.

Explore Other Libraries

X




Copyright (c) 2021 TuteeHUB

OPEN APP
Channel Join Group Join