In mathematics, the logarithm of a number to a given base is the Power or exponent to which the base must be raised in order to produce the number.... with base 10. It is also known as the decadic logarithm, named after its base. It is indicated by log10(x), or sometimes Log(x) with a capital L (however, this notation is ambiguous since it can also mean the complex natural logarithmic multi-valued function). On calculators it is usually "log", but mathematician
Mathematician
A mathematician is a person whose primary area of study and/or research is the field of mathematics.... s usually mean natural logarithm
Natural logarithm
The natural logarithm, formerly known as the hyperbolic logarithm, is the logarithm to the base e , where e is an irrational number constant approximately equal to 2.718281828.... rather than common logarithm when they write "log".
Before the early 1970s, hand-held electronic calculator
Calculator
A calculator is a device for performing mathematical calculations, distinguished from a computer by having a limited problem solving ability and an interface optimized for interactive calculation rather than programming.... s were not yet in widespread use.
In mathematics, the logarithm of a number to a given base is the Power or exponent to which the base must be raised in order to produce the number.... with base 10. It is also known as the decadic logarithm, named after its base. It is indicated by log10(x), or sometimes Log(x) with a capital L (however, this notation is ambiguous since it can also mean the complex natural logarithmic multi-valued function). On calculators it is usually "log", but mathematician
Mathematician
A mathematician is a person whose primary area of study and/or research is the field of mathematics.... s usually mean natural logarithm
Natural logarithm
The natural logarithm, formerly known as the hyperbolic logarithm, is the logarithm to the base e , where e is an irrational number constant approximately equal to 2.718281828.... rather than common logarithm when they write "log".
Before the early 1970s, hand-held electronic calculator
Calculator
A calculator is a device for performing mathematical calculations, distinguished from a computer by having a limited problem solving ability and an interface optimized for interactive calculation rather than programming.... s were not yet in widespread use. Because of their utility in saving work in laborious calculations by hand on paper, tables
Mathematical table
Before calculators were cheap and plentiful, people would use mathematical tables —lists of numbers showing the results of calculation with varying arguments— to simplify and drastically speed up computation.... of base 10 logarithm
Logarithm
In mathematics, the logarithm of a number to a given base is the Power or exponent to which the base must be raised in order to produce the number.... s were found in appendices of many books. 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. There was only a need to include numbers between 1 and 10, since if one wanted the logarithm of, for example, 120, one would know that
The very last number ( 0.079181)—the fractional part of the logarithm of 120, known as the mantissa of the common logarithm of 120—was found in the table. (This stems from an older, non-numerical, meaning of the word mantissa: a minor addition or supplement, e.g. to a text. For a more modern use of the word mantissa, see significand
Significand
The significand is the part of a floating point that contains its significant digits. Depending on the interpretation of the exponent, the significand may be considered to be an integer or a fraction .... .) The location of the decimal point in 120 tells us that the integer part of the common logarithm of 120, called the characteristic of the common logarithm of 120, is 2.
Similarly, for numbers less than 1 we have
The bar over the characteristic indicates that it is negative whilst the mantissa remains positive. Negative logarithm values were rarely converted to a normal negative number (−0.920819 in the example).
The slide rule, also known colloquially as a slipstick, is a mechanical analog computer. The slide rule is used primarily for multiplication and division , and also for "scientific" functions such as Nth roots, logarithms and trigonometry, but does not generally perform addition or subtraction.... s work by using a logarithmic scale
Logarithmic scale
A logarithmic scale is a scale that uses the logarithm of a physical quantity instead of the quantity itself.Presentation of data on a logarithmic scale can be helpful when the data covers a large range of values – the logarithm reduces this to a more manageable range.... .
History
Common logarithms are sometimes also called Briggsian logarithms after Henry Briggs
Henry Briggs (mathematician)
Henry Briggs was an England mathematics notable for changing Napier's logarithms into Common logarithm/Briggesian logarithms.... , a 17th-century British mathematician.
Because base 10 logarithms were most useful for computations, engineers generally wrote "log(x)" when they meant log10(x). Mathematicians, on the other hand, wrote "log(x)" when they mean loge(x) for the natural logarithm. Today, both notations are found. Since hand-held electronic calculators are designed by engineers rather than mathematicians, it became customary that they follow engineers' notation. 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.
Numeric value
The numerical value for logarithm to the base 10 can be calculated with the following identity.
as procedures exist for determining the numerical value for logarithm base e
Natural logarithm
The natural logarithm, formerly known as the hyperbolic logarithm, is the logarithm to the base e , where e is an irrational number constant approximately equal to 2.718281828.... and logarithm base 2
Binary logarithm
In mathematics, the binary logarithm is the logarithm for base 2. It is the inverse function of .... .
The natural logarithm, formerly known as the hyperbolic logarithm, is the logarithm to the base e , where e is an irrational number constant approximately equal to 2.718281828....
In mathematics, the binary logarithm is the logarithm for base 2. It is the inverse function of ....
Alternatively below is a correct but inefficient algorithm written in Python
Python (programming language)
Python is a general-purpose high-level programming language. Its design philosophy emphasizes code readability. Python's core syntax and semantics are Minimalism , while the standard library is large and comprehensive.... that can calculate the common logarithm to an arbitrary number of decimal places.
!/usr/bin/python
from __future__ import division
import math
Calculates the logarithm (of any base > 1) of a positive number
to the an arbitary number of decimal places. The accuracy is
subjected only to limitation of the floating point representation.
def log(X,base=math.e,decimalplace=12):
integer_value=0
while X < 1:
integer_value -= 1
X = X * base
while X >= base:
integer_value += 1
X /= base
decimal_fraction = 0.0
partial = 1.0
# Replace X with X to the 10th power
X **= 10
while decimalplace > 0:
partial /= 10
digit=0
while X >= base:
digit += 1
X /= base
decimal_fraction += digit * partial
# Replace X with X to the 10th power
X **= 10
decimalplace -= 1
return integer_value + decimal_fraction
The slide rule, also known colloquially as a slipstick, is a mechanical analog computer. The slide rule is used primarily for multiplication and division , and also for "scientific" functions such as Nth roots, logarithms and trigonometry, but does not generally perform addition or subtraction....
