Log vs. Ln — What's the Difference?
By Tayyaba Rehman — Published on January 13, 2024
Log is the general logarithm, often base 10 or base e (Ln), while Ln is specifically the natural logarithm with base e (approximately 2.71828).
Difference Between Log and Ln
Table of Contents
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Key Differences
Logarithms are exponents to which a fixed number, the base, must be raised to produce a given number. "Log" commonly represents a logarithm with a base of 10 in general mathematics. For example, log(100) equals 2 because 10 squared is 100.
The notation "Ln" stands for the natural logarithm, which specifically has a base of e, where e is an irrational and transcendental number approximately equal to 2.71828. Ln is prevalent in higher mathematics, particularly in calculus, due to its unique properties when differentiating and integrating.
In practical applications, log is used in many scientific calculations, such as pH in chemistry or the Richter scale in geology, which are based on logarithms of base 10. This makes log an essential concept in a wide range of scientific and engineering disciplines.
Conversely, Ln is critical in pure mathematics, especially where growth processes are analyzed, such as in the case of compound interest in finance or population growth in biology. This makes the natural logarithm indispensable in both theoretical and applied mathematics.
Calculators and computers typically have specific keys or functions for both log and ln, demonstrating their distinct uses. While log is often used in contexts where ratios and orders of magnitude are important, ln is usually applied in continuous growth contexts and in solving time-related problems where e is the base of the exponential function.
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Comparison Chart
Base
Commonly 10 or unspecified
Always e (≈2.71828)
Notation
Log(x)
Ln(x)
Origin of Term
From "logarithm"
Abbreviation for "logarithmus naturalis"
Use in Calculators
Usually labeled as "LOG"
Usually labeled as "LN"
Field of Use
General mathematics, pH levels, decibels
Higher mathematics, calculus, natural processes
Compare with Definitions
Log
A detailed record of events
The captain kept a log of the voyage.
Ln
A function in calculus for differentiation
The derivative of Ln(x) is 1/x.
Log
A unit of wood cut for fuel
He added a log to the fire.
Ln
The natural logarithm function
The value of Ln(1) is always 0.
Log
To enter information in a record
She logged her research findings.
Ln
Integral in solving exponential equations
Ln is used to solve for time in physics.
Log
A usually large section of a trunk or limb of a fallen or felled tree.
Ln
Mathematical concept for growth analysis
Ln helps understand compound interest.
Log
A long thick section of trimmed, unhewn timber.
Ln
A key on scientific calculators
Press Ln to calculate natural logarithms.
Log
A device trailed from a ship to determine its speed through the water.
Ln
Abbreviation of lane
Log
A record of a ship's speed, its progress, and any shipboard events of navigational importance.
Log
The book in which this record is kept.
Log
A record of a vehicle's performance, as the flight record of an aircraft.
Log
A record, as of the performance of a machine or the progress of an undertaking
A computer log.
A trip log.
Log
A logarithm.
Log
To cut down, trim, and haul the timber of (a piece of land).
Log
To cut (timber) into unhewn sections.
Log
To enter in a record, as of a ship or an aircraft.
Log
To travel (a specified distance, time, or speed)
Logged 30,000 air miles in April.
Log
To spend or accumulate (time)
Had logged 25 years with the company.
Log
To cut down, trim, and haul timber.
Log
The trunk of a dead tree, cleared of branches.
They walked across the stream on a fallen log.
Log
Any bulky piece as cut from the above, used as timber, fuel etc.
Log
Anything shaped like a log; a cylinder.
Log
(nautical) A floating device, usually of wood, used in navigation to estimate the speed of a vessel through water.
Log
(figuratively) A blockhead; a very stupid person.
Log
A heavy longboard.
Log
(figuratively) A rolled cake with filling.
Log
(mining) A weight or block near the free end of a hoisting rope to prevent it from being drawn through the sheave.
Log
(vulgar) A piece of feces.
Log
(vulgar) A penis.
Log
A logbook, or journal of a vessel's (or aircraft's) progress.
Log
A chronological record of actions, performances, computer/network usage, etc.
Log
(computer science) Specifically, an append-only sequence of records written to file.
Log
A Hebrew unit of liquid volume (about 3{{nbsp}}liter).
Log
Synonym of logarithm. Category:en:Functions
To multiply two numbers, add their logs.
Log
(sciences) A difference of one in the logarithm, usually in base 10; an order of magnitude.
Log
(transitive) To cut trees into logs.
Log
(transitive) To cut down (trees).
Log
(intransitive) To cut down trees in an area, harvesting and transporting the logs as wood.
Log
(transitive) To make, to add an entry (or more) in a log or logbook.
To log the miles travelled by a ship
Log
(transitive) To travel (a distance) as shown in a logbook.
Log
(transitive) To travel at a specified speed, as ascertained by a chip log.
Log
A Hebrew measure of liquids, containing 2.37 gills.
Log
A bulky piece of wood which has not been shaped by hewing or sawing.
Log
An apparatus for measuring the rate of a ship's motion through the water.
Log
The record of the rate of speed of a ship or airplane, and of the course of its progress for the duration of a voyage; also, the full nautical record of a ship's cruise or voyage; a log slate; a log book.
Log
A record and tabulated statement of the person(s) operating, operations performed, resources consumed, and the work done by any machine, device, or system.
Log
A weight or block near the free end of a hoisting rope to prevent it from being drawn through the sheave.
Log
A record of activities performed within a program, or changes in a database or file on a computer, and typically kept as a file in the computer.
Log
To enter in a ship's log book; as, to log the miles run.
Log
To record any event in a logbook, especially an event relating to the operation of a machine or device.
Log
To engage in the business of cutting or transporting logs for timber; to get out logs.
Log
To move to and fro; to rock.
Log
A segment of the trunk of a tree when stripped of branches
Log
Large log at the back of a hearth fire
Log
The exponent required to produce a given number
Log
A written record of messages sent or received;
They kept a log of all transmission by the radio station
An email log
Log
A written record of events on a voyage (of a ship or plane)
Log
Measuring instrument that consists of a float that trails from a ship by a knotted line in order to measure the ship's speed through the water
Log
Enter into a log, as on ships and planes
Log
Cut lumber, as in woods and forests
Log
A part of a tree trunk
They used a log to create a makeshift bridge.
Log
To travel a certain distance or time
The pilot logged 300 hours of flight time.
Common Curiosities
What does "Ln" represent?
"Ln" represents the natural logarithm with base e.
Why is Ln important in calculus?
Ln has properties that simplify the differentiation and integration of exponential functions.
Is there a relationship between Log and Ln?
Yes, they are related through the change of base formula.
What does "Log" stand for?
"Log" stands for logarithm, usually base 10 or unspecified.
When should I use Log instead of Ln?
Use Log for base 10 logarithms or when the base is not specified, common in general mathematics and practical applications.
Can Log have bases other than 10?
Yes, Log can have any positive base, though base 10 is most common.
Why is e the base for Ln?
The number e (approx. 2.71828) has properties that make it the natural choice for continuous growth processes.
How do you calculate Log and Ln without a calculator?
You can use series expansions or refer to logarithm tables for approximate values.
What is the base of a common Log?
The base of a common Log is typically 10.
Are Log and Ln interchangeable?
No, they are used for different bases and are not interchangeable.
Are Log and Ln used in computer programming?
Yes, programming languages often include functions for both Log and Ln.
Is Ln just a type of Log?
Yes, Ln is a specific type of Log with base e.
What does Log(0) or Ln(0) equal?
Log(0) and Ln(0) are undefined because no number raised to a power will result in zero.
Can you convert between Log and Ln?
Yes, using the formula Log(x) = Ln(x) / Ln(10).
What is the inverse function of Ln?
The inverse function of Ln is the exponential function e^x.
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Written by
Tayyaba RehmanTayyaba Rehman is a distinguished writer, currently serving as a primary contributor to askdifference.com. As a researcher in semantics and etymology, Tayyaba's passion for the complexity of languages and their distinctions has found a perfect home on the platform. Tayyaba delves into the intricacies of language, distinguishing between commonly confused words and phrases, thereby providing clarity for readers worldwide.
