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Transcript of Logarithms
Parts of a logarithm
Base: the number we are multiplying (i.e. 2)
Logarithm: how many times you multiply the base (i.e. 3)
The number we want to get (i.e. 8)
What is a logarithm???
Definition: a quantity representing the power to which a fixed number (the base) must be raised to produce a given number
Simpler form: how many of one
do we multiply to get
Logarithms & Exponents
The logarithm tells you what the exponent is!
By: AJ Foremny, Bobby Reilly, & Jen Stief
Memory Strategy: Mnemonics
Logarithmic and exponential functions are inverses of eachother
Applications: pH (measure acidity), decibels (sound intensity), Richter Scale
Types of Logarithms
Applications: exponential growth & decay models (i.e. compounding), radioctive decay (half-life), population growth
History of Logarithms
Logarithms were originally invented by John Napier in 1614; these did not have bases
The purpose was to simplify multiplication and division to the level of addition and subtraction
Napier and Henry Briggs invented the common system of logarithms 1624
Defining logarithms as exponents wasn't recognized until 1685 by John Wallis
In 1622 English mathematician William Oughtred invented the slide-rule for multiplying and dividing numbers based on logarithms.
Numbers are placed on slide rule scales at distances proportional to the differences between their logarithms. By mechanically adding the distance from 1 to 2 on the lower scale to the distance from 1 to 3 on the upper scale, one can quickly determine that 2 x 3 = 6.
MIT engineers have created synthetic biology circuits that can perform analog computations such as taking logarithms and square roots in living cells.
Logarithms Using a Calculator
Scientific and graphing calculators can quickly calculate logarithms
Flaws of the TI-89
There is no log button. In order to calculate with logarithms, you must:
press CATALOG then find log
press APLHA then type in log
press diamond then 7
Logarithms with Different Bases
To enter a logarithm with a different base on the calculator, use the Change of Base Formula:
When no base is indicated, base 10 is implied. The log key will calculate the common logarithm. 2nd log will calculate the antilogarithm or 10^x.
The ln key calculates the natural logarithm. 2nd ln will calculate e^x.
There is no log button, but there is a LOG menu!