E-Lecture - Logarithms
The logarithm of a number is the index or exponent by which another value must be raised to produce an equivalent value of the given number. For example, in the indicial expression, 43 = 64, the base is 4 and the index or exponent is 3. We write this expression in logarithm as log4 64 = 3.
We read this as “logarithm of 64 to the base 4 is 3.”
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Historical Note |
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Logarithms were developed in the 17th century by the Scottish mathematician, John Napier (1550 – 1617). He was the first mathematician to devise the idea of the logarithm, naming it logarithm from the Greek root’s logos, meaning proportion and arithmus meaning number because he used it to relative numbers to another value. The logarithm has changed very much since its introduction into the world of mathematics, it began as a way to make the multiplication and division of large numbers into an easier form looking up value in a table and them adding them for multiplication and subtracting them for division and from there it has evolved into the logarithm known today as the inverse of the exponent. |
In general, for a fixed positive number b ≠ 1 and for every real number a > 0
c = logb a if and only if bc = a.
From the above statement, we can note that every logarithmic statement can be converted into an indicial (exponential statement) and vice versa.
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