Logarithm

The Logarithm of a given number to a given base is the index of the power to which the base must be raised in order to equal the given number
1. When base is 'e' , then the logarithmic function is called natural logarithmic function
2. When base is '10' , then the logarithmic function is called common logarithmic function
Characteristic and Mantissa
1. The integer part of a Logarithm is called the characteristic and the fractional part is called mantissa.
Log₁₀ N = integer(characteristic) + fraction(mantissa) 2. The mantissa part of a log of a number is always kept positive.
3. The characteristic of Log₁₀ N be n , then the number of digits in N is (n+1).
Properties of Logarithms
1. log_aa = 1 , log_a1 = 0
2. log_ab.log_ba = 1 ⇒
3 log_ca = log_ba.log_cb or
4. log_a(mn) = log_am + log_an
5.
6. log_amⁿ = nlog_am
7. a^log_am = m
8.
9.
Practice set 1 Practice set 2

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Logarithm | free study material for IIT-JEE , NDA and Airforce