Exponential Notation (Logarithm)

The short-hand notation of a very large or very small number expressed in power 10 is called exponential Notation. The mass of electron is 0.000 000 000 000 000 000 000 000 000 911g, this can be written by exponential notation as 9.11x10-28g. The number of atoms present in 1mole of elements is found to be 602,300,000,000,000,000,000,000 which can be written as 6.023x1023. In Exponential terms, 10 is called the base. The power to base is called exponent or logarithm. There are two methods of determining the exponents of 10.
1) When decimal point shifted towards right side, the exponent of 10 is always negative in such a case.
Example: 0.00016 can be expressed as 1.6x10-4.
2) When decimal point shifted toward left side, the exponent of 10 is always positive in such a case.
Example: 16000 can be expressed as 1.6x104.
 In the expression, ax=y is called the logarithm of y to the base a, where a must be positive number other than one. In logarithm the base is usually 10.

The logarithm is divided into two parts:
1) Mantissa: The part of a logarithm after the decimal point is called mantissa; it is always positive and less than 1. 
2) Characteristics: The integer part of logarithm is called characteristics; it can be positive or negative.
Example: Log 273 = 2.4362  
Here Characteristic 273 = 2    and     mantissa 273 = 0.4362

The Use of Logarithms in Computations
There are three fundamental rules in logarithm.
1) Log (a x b) = log a + log b
2) Log (a/b) = log a – log b
3) Log (a)n = n log a
Where a and b are any two positive numbers and n is any positive or negative number.
 

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