The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: 1000 = 10 × 10 × 10 = 103. More generally, if x = by, then y is the logarithm of x to base b, and is written y = logb(x), so log10(1000) = 3. Logarithms were introduced by John Napier in the early 17th century as a means to simplify calculations. They were rapidly adopted by navigators, scientists, engineers, and others to perform computations more easily, using slide rules and logarithm tables. Tedious multi-digit multiplication steps can be replaced by table look-ups and simpler addition because of the fact — important in its own right — that the logarithm of a product is the sum of the logarithms of the factors: The present-day notion of logarithms comes from Leonhard Euler, who connected them to the exponential function in the 18th century. The logarithm to base b = 10 is called the common logarithm and has many applications in science and engineering. The natural logarithm has the constant e (≈ 2.718) as its base; its use is widespread in pure mathematics, especially calculus. The binary logarithm uses base b = 2 and is prominent in computer science. Logarithmic scales reduce wide-ranging quantities to smaller scopes. For example, the decibel is a logarithmic unit quantifying sound pressure and voltage ratios. In chemistry, pH is a logarithmic measure for the acidity of an aqueous solution. Logarithms are commonplace in scientific formulae, and in measurements of the complexity of algorithms and of geometric objects called fractals. They describe musical intervals, appear in formulae counting prime numbers, inform some models in psychophysics, and can aid in forensic accounting. In the same way as the logarithm reverses exponentiation, the complex logarithm is the inverse function of the exponential function applied to complex numbers. The discrete...

...addition, subtraction and a table of squares. However it could not be used for division without an additional table of reciprocals. Large tables of quarter squares were used to simplify the accurate multiplication of large numbers from 1817 onwards until this was superseded by the use of computers.
Michael Stifel published Arithmetica integra in Nuremberg in 1544, which contains a table of integers and powers of 2 that has been...

...the points for insect wings would be jammed up against one side.
Now, instead of plotting length, what if we plot the logarithm of length? There will be as much space on the graph between 0.1 inch and 1 inch as there is between 100 inches and 1000 inches, because
log(0.1) = -1
log(1) = 0
log(100) = 2
log(1000) = 3
So the graph will be much easier to read.
Logarithms are used in a lot of places to scale numbers when there's a big range between the...

...Mrs. Cappiello
Algebra 2/Trig, Period 6
1 April 2012
Exponents and Logarithms
An exponent is the number representing the power a given number is raised to. Exponential functions are used to either express growth or decay. When a function is raised to a positive exponent, it will cause growth. However, when a function is raised to a negative exponent, it will cause decay. Logarithms work differently than exponents. Logarithms represent what power...

...CHAPTER 2
EXPONENTIAL AND LOGARITHMS FUNCTIONS (534)
2.1 Exponential functions and their graph
Definition
An exponential function with base b is defined by the equation
[pic] Or [pic] ([pic] [pic]and x is a real number)
The domain of any exponential function is the interval ([pic] The range is the interval [pic]
Example 1: Graph the exponential function [pic]
Example 2: Graph the exponential function [pic]
Properties of...

...the following:
4.
5. Convert to log form
6. Evaluate the logarithm without a calculator:
7. Solve the following equations:
8. Fill in the chart and graph:
x
1/4
1/2
0
2
4
8
16
9. A biologist is researching a newly-discovered...

...History of LogarithmsLogarithms were invented independently by John Napier, a Scotsman, and by Joost Burgi, a Swiss. Napier's logarithms were published in 1614; Burgi's logarithms were published in 1620. The objective of both men was to simplify mathematical calculations. This approach originally arose out of a desire to simplify multiplication and division to the level of addition and subtraction. Of course, in this era of the cheap...

...
PRINCE ALFRED COLLEGE
YEAR 10 ADVANCED MATHEMATICS
TEST 4: Part 2
Thursday 12-08-09
TOPIC: Indices (Exponents) & Logarithms & modelling
Name:
Pastoral Care Group: 10
Maximum mark
Your mark
Grade
% mark
Class
average...

...Logarithm Base
IB Math SL
Type I Portfolio
Lisa Phommaseng
Logarithm Base
Consider the given sequences:
Log28, log48, log88, log 168, log328,…
Log381, log981, log 2781, log8181,…
Log525, log2525, log12525, log62525,…
:
:
:
,…
For the first sequence Log28, log48, log88, log 168, log328,… you are to find the next two terms of each of the sequences you would have to determine the pattern. As we can see, the value of the bases, 2,4,8,16,32 are...