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Topic: Natural logarithm

Related Topics

Natural log

Logarithmic integral function

Logarithmic integral

Logarithm

Antilogarithm

Common logarithm

Common logarithm

Exponential function

Inverse function

Binary logarithm

Exponent

Integration by parts

Differential calculus

	PlanetMath: natural logarithm
		The natural logarithm of a number is the logarithm in base of Euler's number
		Therefore the logarithm we defined is not continuous at -1.
		This is version 9 of natural logarithm, born on 2002-02-25, modified 2006-10-02.
	planetmath.org /encyclopedia/NaturalLogarithm2.html (307 words)

	The educational encyclopedia, mathematics, algebra, Logarithms and exponentials
		Exponential and logarithmic functions exponentials, e, the derivative of the exponential function, logarithms, the derivative of the natural logarithm, exponential growth
		Logarithmic scales to introduce you to the concept of logarithmic scales, and in particular to the decibel scales commonly used in acoustics to measure loudness
		Natural logarithm natural logarithm, the natural logarithm ln x is the logarithm having base e, where e = 2,718281...
	www.educypedia.be /education/mathlogarithms.htm (275 words)

	Natural logarithm - ExampleProblems.com
		The natural logarithm, invented by John Napier, is the logarithm to the base e, where e is equal to 2.71828...
		On hand-held calculators the natural logarithm is ln, whereas log is the base-10 logarithm.
		Logarithms can be defined to any positive base other 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.exampleproblems.com /wiki/index.php?title=Natural_logarithm&printable=yes (966 words)

	Logarithm Summary
		Logarithms to various bases: red is to base e, green is to base 10, and purple is to base 1.7.
		Therefore, logarithms are useful for making lengthy numerical operations easier to perform and, before the advent of electronic computers, they were widely used for this purpose in fields such as astronomy, engineering, navigation, and cartography.
		This he followed, in 1624, by his Arithmetica Logarithmica, containing the logarithms of all integers from 1 to 20,000 and from 90,000 to 100,000 to fourteen places of decimals, together with a learned introduction, in which the theory and use of logarithms are fully developed.
	www.bookrags.com /Logarithm (4345 words)

	math lessons - Natural logarithm
		The natural logarithm is the logarithm to the base e, where e is approximately equal to 2.71828...
		Logarithms can be defined to any positive base other 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.
		Second, expressions in which the unknown variable appears as the exponent of e occur much more often than exponents of 10 (because of the "natural" properties of the exponential function which allow it to describe growth and decay behaviors), and so the natural logarithm is more useful in practice.
	www.mathdaily.com /lessons/Natural_logarithm (1019 words)

	Common Logarithm
		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.
		So ironically, that notation, according to which one writes "ln(''x'')" when the natural logarithm is intended, may have been further popularized by the very invention that made the use of "common logarithms" far less common, electronic calculators.
	www.seattleluxury.com /encyclopedia/entry/common_logarithm (603 words)

	Logarithm transformation
		By taking logarithms of variables which are multiplicatively related and/or growing exponentially over time, we can often explain their behavior with linear models.
		However, in Excel and many hand-held calculators, the natural logarithm function is written as LN instead, and LOG stands for the base-10 logarithm.
		Trend in logged units = percentage growth: Because changes in the natural logarithm are (almost) equal to percentage changes in the original series, it follows that the slope of a trend line fitted to logged data is equal to the average percentage growth in the original series.
	www.duke.edu /~rnau/411log.htm (1001 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)

	VIC Natural logarithm. Natural exponential.
		The "natural logarithm" function, ln, was the solution to the differential equation L'(t) = 1/t with L(1) = 0, while the "natural exponential" function, exp or e, was the solution to the differential equation P'(t) = P(t) with P(0) = 1.
		For both these reasons we say that the natural logarithm and natural exponential function are inversely related as functions.
		Thus if (a,b) is a point on the graph of the natural exponential function, then (b,a) is a point on the graph of the natural logarithm function.
	www.humboldt.edu /~mef2/book/VIC.htm (776 words)

	SparkNotes: SAT Subject Test: Math Level 2: Logarithms
		A logarithm is the power to which you must raise a given number, called the base, to equal another number.
		Unless the logarithm is a very simple one, you won’t be able to mentally calculate it—so the calculator becomes an important tool.
		Natural logarithms appear on the Math IIC but not on the Math IC test.
	www.sparknotes.com /testprep/books/sat2/math2c/chapter4section10.rhtml (650 words)

	Demystifying the Natural Logarithm (ln) \| BetterExplained
		Given how the natural log is described in math books, there’s little “natural” about it: it’s defined as the inverse of e^x, a strange enough exponent already.
		Natural Log (ln) is the amount of time needed to reach a certain level of growth.
		The natural log is the inverse of e, a fancy term for opposite.
	betterexplained.com /articles/demystifying-the-natural-logarithm-ln (2807 words)

	Function Grapher Online
		Square root of argument (number or expression inside the parentheses).
		Natural logarithm of argument (base-E logarithm of argument where E is Euler's constant)
		Base-2 logarithm of E (E: see above), is 1.4426950408889633...
	www.walterzorn.com /grapher/grapher_e.htm (449 words)

	S.O.S. Mathematics CyberBoard :: View topic - Question regarding Natural Logarithm and Exponential fns
		Posted: Tue, 17 Oct 2006 15:20:29 GMT Post subject: Question regarding Natural Logarithm and Exponential fns
		I'm not completely convinced that this is the right forum to place this question, but here goes.
		I'm confused because I thought that not only should the exponent c be applied to the constant 2, but that by definition, applying the exponential function to a logarithmic function left you with the value
	www.sosmath.com /CBB/viewtopic.php?t=25691 (224 words)

	Integral Form of the Definition of Natural Logarithm ln(x) (Site not responding. Last check: )
		Integral Form of the Definition of Natural Logarithm ln(x)
		This is an applet to explore the definition of the natural logarithm ln(x).
		The integral is computed numerically using Simpson's rule.
	www.analyzemath.com /calculus/LogDefinition/LogDefinition.html (194 words)

	Logarithm
		The logarithm, therefore, of any sine is a number very neerely expressing the line which increased equally in the meene time whiles the line of the whole sine decreased proportionally into that sine, both motions being equal timed and the beginning equally shift.
		The logarithm of the number 70 is 1.84510, and the logarithm of the number 700 is 2.84510.
		Logarithms had reached their full potential and most of what was done after 1694 was calculating logarithms to different bases.
	www.thocp.net /reference/sciences/mathematics/logarithm_hist.htm (1934 words)

	Natural logarithm - Wikinfo
		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 (3157 words)

	Glossary of Fish Related Terms
		Instantaneous Rate Of Fishing Mortality -- When fishing and natural mortality act concurrently, F is equal to the instantaneous total mortality rate, multiplied by the ratio of fishing deaths to all deaths.
		Instantaneous Rate Of Natural Mortality -- When natural and fishing mortality operate concurrently it is equal to the instantaneous total mortality rate, multi- plied by the ratio of natural deaths to all deaths.
		Naturally spawning populations -- Populations of fish that have completed their entire life cycle in the natural environment without human intervention.
	www.streamnet.org /pub-ed/ff/Glossary/glossaryfish.html (5781 words)

	Reference.com/Encyclopedia/Natural logarithm
		The natural logarithm, formerly known as the hyperbolic logarithm, is the logarithm to the base e, where e is a certain constant approximately equal to 2.718281828459.
		Logarithms can be defined to any positive base other than 1, not just e, and are useful for solving equations in which the unknown appears as the exponent of some other quantity.
		The reason we call the ln(x) "natural" is twofold: first, expressions in which the unknown variable appears as the exponent of e occur much more often than exponents of 10, and second, because the natural logarithm can be defined quite easily using a simple integral or Taylor series--which is not true of other logarithms.
	www.reference.com /browse/wiki/Natural_logarithm (1297 words)

	Logarithms - Topics in precalculus
		Logarithms replace a geometric series with an arithmetic series.
		To indicate the natural logarithm of a number, we use the notation "ln."
		"The logarithm of a quotient is equal to the logarithm of the numerator
	www.themathpage.com /aPreCalc/logarithms.htm (705 words)

	Logarithm Table
		the logarithm must be computed to look for the electric current which flows through the circuit.
		At the electronic circuits, the common logarithm(the logarithm having base 10) is used for the thing except above-mentioned natural logarithm.
		The common logarithm is used for the dB (decibel).
	www.interq.or.jp /japan/se-inoue/e_logarithm.htm (292 words)

	Logarithms
		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.
		If the logarithm to the base b of x is equal to y, then b raised to the y power will give you the value x.
	hyperphysics.phy-astr.gsu.edu /hbase/logm.html (187 words)

	Integrals (Site not responding. Last check: )
		Since the natural logarithm of e is 1, the integral of e^(x) is e^(x).
		The integral of the secant of x is the natural logarithm of the sum of the secant of x and the tangent of x.
		The integral of the cosecant of x is the opposite of the natural logarithm of the sum of the cosecant of x and the cotangent of x.
	www.gomath.com /htdocs/ToGoSheet/Calculus/integrals/integrals.html (242 words)

	logshtml6-4-99
		Therefore, the logarithm of a number (y) is the power (x) to which the base must be raised to equal that number.
		With e = 2.718…, the natural logarithm of a number is not as straightforward as with common logarithms.
		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/index.html (1334 words)

	The number e
		This was in 1618 when, in an appendix to Napier's work on logarithms, a table appeared giving the natural logarithms of various numbers.
		Perhaps surprisingly, since this work on logarithms had come so close to recognising the number e, when e is first "discovered" it is not through the notion of logarithm at all but rather through a study of compound interest.
		We mentioned above that logarithms were not thought of in the early years of their development as having any connection with exponents.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/e.html (1655 words)

	Exponential and Logarithmic Functions - e and the Natural Logarithm (Site not responding. Last check: )
		Exponential and logarithmic functions with base e occur in many practical applications, including those involving growth and decay, continuous compounding of interest, alternating currents and learning curves.
		The natural logarithm of a positive real number is defined as the logarithm to the base e of the number.
		The natural logarithm possesses the same properties as common logarithms.
	library.thinkquest.org /10030/9eatnln.htm (183 words)

	Properties of Logarithms: Solutions
		Determine which rule of logarithms was used to go from the first equation to the second, and how it was used (i.e., match up the variables in the formula for the rule and the corresponding expressions in the equation), or
		Repeat this Exercise as often as necessary until you are confident in your ability to correctly apply the rules of logarithms.
		Repeat this Exercise as often as necessary until you are confident in your ability to correctly apply the rules of logarithms to solve exponential equations.
	campus.northpark.edu /math/precalculus/Transcendental/Logarithmic/properties/exercises/solutions.html (1098 words)

	No Title
		Simple exponential functions can always be written as a logarithmic function, where the base of the logarithm is the same as the base of the exponential function.
		Logarithmic and exponential functions are inverses IF and ONLY IF the two functions have the exact same base.
		Because the base of the natural logarithm is e, we chose our exponential function to have base e.
	www-math.cudenver.edu /~rrosterm/review/review.html (452 words)

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