College Math Phase 4(B)

Logarithms

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TABLE OF CONTENTS

Introduction 2

Common Logarithm 2

Natural Logarithm 2

Easier Calculations 3

Applications of Logartihms 4

References 5

In the field of mathematics , getting the logarithmic value of x with respect to a base number is equivalent to the base number raised to the power of the value of the logarithm (Berggren Singer , 2007 . This is best expressed as y logbase x is equal to x basey . Analyzing the two equations , the value of the logarithm

y in the first equation is simply the exponent of the base number in the second . Just as any mathematical equation can be manipulated to show different expressions of the same equation , logarithms are just another way of expressing exponential values . Almost every book on mathematics gives credit to John Napier as the mathematician that developed the different theories and methodologies that comprise logarithms . While this may be correct another fellow by the name of Joost Burgi actually was the first to come up with the logarithmic computations as he needed the data in his study of astronomy . Burgi came up with his study a full decade earlier than Napier 's version . He published his study in 1620 , six years later than Napier ( Science and its times

Common Logarithm

The base value of an exponent can be a wide variety of numbers but the most commonly used bases are the 10 , called common logarithm , and the e called natural logarithm . Common logarithms or often denoted as log10 or lg . Common logarithms are generally used in pure and applied mathematics (Berggren Singer , 2007 . Prior to the age of computers and calculators , tables were used to find the common logarithm of different values to shorten computation times . The first table of the sort was developed by Henry Briggs (Berggren Singer , 2007 . Common logarithms are used to solve for ratios when the values in question are too large or too small

Natural Logarithm

Logarithms with a base of e are natural logarithms . e in this case takes the approximate value of 2 .71828 . To differentiate itself from log , natural logarithms take the symbol of ln , an abbreviation from the latin words logarithmus naturali . A natural logarithm or ln is the inverse of ex ( Demystifying , 2007 ) and more commonly used in applications that require for the computation of growth rates

Easier Calculations

One benefit of logarithms is easier calculation . Not that anything in mathematics is easy but results of values that undergo logarithmic computation are more manageable than straight forward arithmetic . The decibel is an example of how very large or very small values can be more accurately translated , making the mathematical problem easier to manage Decibels are nothing more than logarithmic ratios of two values . In a communications system for example , if a transmitter inputs 10 watts of power and outputs 1 microwatt . In linear ratios , Power out versus power in is equal to 0 .0000001 . In decibel form , which is given by the equation

10log10 (Power out /Power...