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Topic: Common logarithm

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In the News (Thu 18 Apr 19)

In mathematics, the logarithm functions are the inverses of the exponential functions.
Before the widespread availability of electronic computers, logarithms were widely used as a calculating aid, both with tables of logarithms and slide rules.
Logarithms are also useful in order to solve equations in which the unknown appears in the exponent, and they often occur as the solution of differential equations because of their simple derivatives.
www.ebroadcast.com.au /lookup/encyclopedia/lo/Logarithmic.html   (420 words)

 Common logarithm - Wikipedia, the free encyclopedia   (Site not responding. Last check: 2007-11-05)
In mathematics, the common logarithm is the logarithm with base 10.
Such a table of "common logarithms" giving the logarithm of each number in the left-hand column, which ran from 1 to 10 by small increments, perhaps 0.01 or 0.001.
Common logarithms are sometimes also called Briggsian logarithms after Henry Briggs, a 17th-century British mathematician.
en.wikipedia.org /wiki/Common_logarithm   (601 words)

 Logarithm   (Site not responding. Last check: 2007-11-05)
Logarithm is the exponent or power to which a base must be raised to yield a given number.
When a common logarithm of a number is written as the sum of an integer and a positive decimal (e.g., 2.3147), the integer--called the characteristic--serves to locate the decimal point in the number, and the decimal--called the mantissa--indicates the digits in the number.
The latter are determined from tables of logarithms, which relate mantissas to numbers.
abyss.uoregon.edu /~js/glossary/logarithm.html   (244 words)

 Bryn Mawr College: Survival Skills for Problem Solving   (Site not responding. Last check: 2007-11-05)
The common logarithm (written: log x) of a number is the power to which 10 must be raised to equal that number.
Logarithms for numbers are generally found using a calculator since the relationship between a number and its logarithm is not generally obvious.
Natural logarithms (written: ln x) are identical to common logarithms, except the natural log of a number is the power to which e (2.718...) must be raised to get that number.
www.brynmawr.edu /nsf/tutorial/ss/sslog.html   (421 words)

 How Did a Slide Rule Work?
Thus, 4 is 2 to the second power, 8 is 2 to the third power, 16 is 2 to the fourth power, and 2 is the logarithm of 4 to the base 2, 3 is the logarithm of 8 to the base 2, and 4 is the logarithm of 16 to the base 2.
This makes them convenient for doing arithmetic, because the integer part of a common logarithm indicates where to put the decimal point, and the fractional part is the same for the logarithm of 326, 32.6, or 3.26, so that tables need only contain the fractional part of a common logarithm.
The L scale is a uniform linear scale, and is used to read off the fractional portion (or mantissa) of the common logarithm of numbers on the C scale.
www.quadibloc.com /math/slrint.htm   (1438 words)

 Logarithms   (Site not responding. Last check: 2007-11-05)
Although a logarithm may be defined with any base, the logs most often encountered are the logarithm to the base 10 which is called the common logarithm
Logarithms may be manipulated with the combination rules.
The logarithm to the base b of the variable x is defined as the power to which you would raise b to get x.
hyperphysics.phy-astr.gsu.edu /hbase/logm.html   (187 words)

The base of a logarithm can be any positive real number other than 1, but when the base is 10 the logarithm is called a common logarithm or a common log.
Sometimes, a chart or graph uses a logarithmic scale for only one of two axes, in which cases it is called a semi-logarithmic.
Logarithmic scales are also useful in charts and graphs, especially when the rate of change is geometric.
www.bsu.edu /web/jcflowers1/rlo/mathlogarithms.htm   (1000 words)

 Wikinfo | Natural logarithm
The natural logarithm is the logarithm to the base e, where e is approximately equal to 2.71828...
Most of the reason for thinking about base-10 logarithms became obsolete shortly after about 1970 when hand-held calculators became widespread (for more on this point, see common logarithm).
Logarithms can be defined to any positive base greater than 1, not just e, and they are always useful for solving equations in which the unknown appears as the exponent of some other quantity.
www.wikinfo.org /wiki.php?title=Natural_logarithm   (978 words)

 Logarithm   (Site not responding. Last check: 2007-11-05)
A common logarithm is a logarithm to the base 10.
Thus, the common logarithm of 100 (log 100) is 2, because.Logarithms to the base, in which called natural logarithms, are especially useful in calculus.
Logarithms were invented to simplify cumbersome calculations, since exponents can be added or subtracted to multiply or divide their bases.
www.cbv.ns.ca /mathhelp/logarithm1.htm   (70 words)

 KryssTal : A Look At Logarithms
Logarithms turned out to be one of the most important aids to computation before the arrival of computers and calculators.
Remember, logarithms are really indices so the laws are similar to the laws of indices.
Logarithms can be used to solve algebraic equations where the unknown is in the index.
www.krysstal.com /logarithms.html   (1248 words)

 logshtml6-4-99   (Site not responding. Last check: 2007-11-05)
Logarithmic mathematical relationships between various quantities occur very frequently when dealing with the quantitative aspects of almost all fields of science.
Therefore, the logarithm of a number (y) is the power (x) to which the base must be raised to equal that number.
Logarithms or antilogarithms of such numbers must be determined with the aid of a logarithm table of a pocket calendar with a log x, ln x, x
www.umd.umich.edu /casl/natsci/slc/slconline/LOGS   (1334 words)

 Cube root via logarithms   (Site not responding. Last check: 2007-11-05)
Common logarithms refer to logarithms where the base is 10.
However, since the table of logarithms or antilogarithms listed each number only in four digits, we were only able to get cube roots with precision of at most four digits using logarithms.
Since the advent of calculators that also have a key for finding the antilogarithm, the precision came to be limited by one less than the number of digits given by the calculator.
www.mathpath.org /Algor/cuberoot/cube.root.logarithms.htm   (228 words)

This is just an identity arising from the definition of the logarithm, but it is sometimes useful in manipulating formulas.
The integer part is called the characteristic of the logarithm, and the fractional part is called the mantissa.
Logarithms were used in the days before computers to perform multiplication of large numbers.
ccrma-www.stanford.edu /~jos/mdft/Logarithms.html   (359 words)

 Common Logarithms
Thus the natural logarithm of 1.60 is 0.4700, correct to four significant digits.
Referring to table 8-3, notice that the logarithm of 1 is 0 and the logarithm of 10 is 1.
logarithm of a number is nothing more than expressing the number as a power of 10.
www.tpub.com /math1/9a.htm   (383 words)

 The Power in Numbers\\A Logarithms Refresher
Logarithms are defined in such a ''backwards'' way that sometimes students see only the rules for using them, and can't get a good picture of what they are.
The common logarithm of 3 is (to five figures, at least) 0.47712.
All the ''rules'' of logarithms are the same, whether we use 10 as a base (common logarithms) or e as a base (natural logarithms).
www.math.unh.edu /mac/calc/power.html   (2010 words)

 Chemistry 106 Logs Part I
The first step in determining a logarithm of a number is to write the number in exponential form as a coefficient (the value ranging from 1.000 to 9.9999...) and ten raised to some power.
Logarithms are used extensively in the area of acid-base chemistry and biology.
The common logarithm (log) uses the base 10, that is, a logarithm was the number to which 10 must be raised to give a specific number.
web.uccs.edu /SLC/modules/chem106/c106logs1.htm   (1648 words)

 Logarithmic Functions   (Site not responding. Last check: 2007-11-05)
Before the advent of calculators, first tables of logarithms and then slide rules based on logarithms were used as an aid to multiplication.
The natural logarithm is the one which has the nicest purely mathematical properties and is the one which we use almost exclusively in calculus.
The common logarithm of x, often written simply as log x, is the logarithm to the base 10.
oregonstate.edu /instruct/mth251/cq/FieldGuide/logarithmic/lesson.html   (284 words)

 Logarithms - Topics in precalculus
In any base, the logarithm of the base itself is 1.
Logarithms replace a geometric series with an arithmetic series.
"The logarithm of a quotient is equal to the logarithm of the numerator
www.themathpage.com /aPreCalc/logarithms.htm   (699 words)

 Logarithm Sp 99   (Site not responding. Last check: 2007-11-05)
Logarithm is the exponent to which a number is raised to produce a given number.
The common logarithm, commonly abbreviated as log, refers to the exponent to which 10 has to be raised, and the natural logarithm, abbreviated ln, refers to the exponent to which e has to be raised.
Logarithm of more complex numbers require the use of a calculator or a log table.
www.towson.edu /~yau/LogarithmSp99.htm   (1716 words)

 Logarithmic Functions
There are several properties of logarithmic functions that follow easily from the definition and are evident from the graphs in the applet above.
It follows that its inverse, the logarithm with base e, is the most important of the logarithmic functions.
The logarithm with base e is called the natural logarithm, and it is denoted ln.
www.uncwil.edu /courses/mat111hb/EandL/log/log.html   (673 words)

 Logarithm Tutorial   (Site not responding. Last check: 2007-11-05)
The logarithm is a mathematical function much the same as more familiar functions such as the square root, sin, or absolute value functions.
One important difference between the logarithm function and most other mathematical functions is that there are different varieties or flavors of the logarithm function.
First, the scale of the logarithmic axis represents the log of a variable; however, the axis is labeled using the values of the original variable.
aghort.nmsu.edu /soils/soil_physics/tutorials/log/log_home.html   (1906 words)

 Common Logarithm -- from Wolfram MathWorld
is used to denote a base-10 logarithm, which conflicts with the use of the symbol lg to indicate the logarithm to base 2.
is used for the logarithm to the base 2.
The common logarithm extended into the complex plane is illustrated above.
mathworld.wolfram.com /CommonLogarithm.html   (205 words)

 All Elementary Mathematics - Study Guide - Algebra - Logarithms...
A consequence of this property is the following: logarithm of a root is equal to the logarithm of radicand divided by the degree of the root:
Logarithms of the rest of the numbers have a fractional part, called a mantissa.
Common logarithms are the most suitable for practical use.
www.bymath.com /studyguide/alg/sec/alg30.html   (372 words)

 Properties of Logarithms
While most scientific calculators have buttons for only the common logarithm and the natural logarithm, other logarithms may be evaluated with the following change-of-base formula.
The change-of-base formula allows us to evaluate this expression using any other logarithm, so we will solve this problem in two ways, using first the natural logarithm, then the common logarithm.
Logarithms break products into sums by property 1, but the logarithm of a sum cannot be rewritten.
www.uncwil.edu /courses/mat111hb/EandL/logprop/logprop.html   (255 words)

 Logarithm - Wikipedia, the free encyclopedia
Logarithms are useful in solving equations in which exponents are unknown.
The discovery of logarithms just before Newton's era had an impact in the scientific world which can be compared with the invention of the computer in the 20th century, because many calculations which were too laborious became feasible.
When the chronometer was invented in the 18th century, logarithms allowed all calculations needed for astronomical navigation to be reduced to just additions, speeding the process by one or two orders or magnitude.
en.wikipedia.org /wiki/Logarithm   (2706 words)

 Common Terms in Mathematics [Dilara & M.Tevfik Dorak]
Common denominator: A denominator that is common to all the fractions within an equation.
Logarithm: The logarithm of a number N to a given base b is the power to which the base must be raised to produce the number N. Written as log
Lowest common multiple (LCM): The smallest non-zero natural number that is a common multiple of two or more natural numbers (compare with the highest common factor).
dorakmt.tripod.com /mtd/glosmath.html   (2892 words)

 BioMath: Logarithmic Functions
In the biological sciences, you are likely to encounter the base 10 logarithm, known as the common logarithm and denoted simply as log; and the base e logarithm, known as the natural log and denoted as ln.
Computing the common logarithm of x > 0 by hand can only be done under special circumstances, and we will examine these first.
Since exponential and logarithmic functions are inverses, the domain of logarithms is the range of exponentials (i.e.
www.biology.arizona.edu /biomath/tutorials/Log/Definitionlredit.html   (692 words)

 Logarithm -- from Wolfram MathWorld
Logarithms are used in many areas of science and engineering in which quantities vary over a large range.
For example, the decibel scale for the loudness of sound, the Richter scale of earthquake magnitudes, and the astronomical scale of stellar brightnesses are all logarithmic scales.
If the logarithm is taken as the forward function, the function taking the base to a given
mathworld.wolfram.com /Logarithm.html   (414 words)

 exponential function
The inverse of the exponential function is the logarithmic function or logarithm.
For 10 as the base of the logarithm we've got the common logarithm log(x), also called Briggs' logarithm or Briggian logarithm.
For 2 as the base of the logarithm the binary logarithm lb(x) is the case.
www.2dcurves.com /exponential/exponentiale.html   (869 words)

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