Question 62400: explain the elemetary concept of logarithm by quoting simple example for beginner student. Why to use logarithms and how? what is the use?
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! explain the elemetary concept of logarithm by quoting simple example for beginner student. Why to use logarithms and how? what is the use?
LET ME GIVE YOU THE USES FIRST.
IN CARRYING OUT MATHEMATICAL OPERATIONS,WE KNOW THAT THESE ARE IN INCREASING ORDER OF DIFFICULTY
1.ADDITION/SUBTRACTION
2.MULTIPLICATION/DIVISION
3.FINDING POWERS/ROOTS
HENCE IF WE CAN CONVERT PROBLEMS IN FINDING
1.POWERS/ROOTS TO MULTIPLICATION/DIVISION...AND
2.MULTIPLICATION/DIVISION TO ADDITION/SUBTRACTION..
THEN THIS HELPS US GREATLY IN CARRYING OUT THE ARITHMATIC COMPUTATION.OF COURSE THIS WAS FOR WORK WITHOUT SLIDERULES/CALCULATORS/COMPUTERS
EVEN OTHER WISE IN HIGHER ALGEBRA - CALCULUS ETC..WE NEED LOGARITHMS PARTICULARLY TO BASE 'E' WHICH PLAY A GREAT PART THERE.
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NOW ON TO LOGS
YOU KNOW POWERS I SUPPOSE
WE SAY 3^2 = 9...BECAUSE 3*3=9
INGENERAL B^P=N SAY
THEN WE SAY THAT
LOGARITHM OF N TO BASE B = P THE POWER.
WE ALWAYS GO BACK TO THIS DEFINITION TO UNDERSTAND LOGS.
WE SAY ANTILOG OF P TO BASE B IS N.
THOUGH ANY BASE CAN EXIST AS PER ABOVE DEINITION,FOR STANDARDISATION 2 BASES
NAMELY 10 AND E = APPROXIMATELY 2.7 ARE TKEN AND TABLES ARE MADE FOR THESE BASES,BOTH FOR LOGS AND ANTI LOGS.THEN COMPUTATIONS ARE DONE AS OUT LINEDBELOW.
YOU WILL LEARN IN THIS TOPIC THAT BY USE OF LOGS OUR ABOVE OBJECTIVE IS FULFILLED AS FOLLOWS.
LOG(X*Y)=LOG(X)+LOG(Y)...MULTIPLICATION TO ADDITION
LOG(X/Y)=LOG(X)-LOG(Y)...DIVISION TO SUBTRACTION
LOG(X^N)=N*LOG(X).....POWERS TO MULTIPLICATION
LOG(NTH.ROOT OF X) = [LOG(X)]/N...ROOTS TO DIVISION.
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