Revision Notes: Logarithms | Mathematics Class 9 ICSE PDF Download

Related terms 

•  Let a, b, c are three numbers and they are related so that a^b = c; then exponent, 'b' is called the logarithm of number, 'c' to the base 'a', and  log_a c = b
• Definition of logarithm: Thus, logarithm of any number to a given base is equal to the index to which the base should be raised to get the given number.  

Important concepts

• The exponential form: a^b = c
• Logarithmic form: log_a c = b
• x₀ = 1 ⇒ log_x 1 = 0
• Logarithm of 1 to any base is zero. 
• Since, a¹ = a, log_a a = 1
• Logarithms to the base 10 are known as common logarithms. 
• If no base is given, the base is always taken as 10. 

Laws of Logarithms  

• First law (product law): The logarithm of a product is equal to the sum of the logarithms of its factors. 
  log_a (m x n) = log_a m + log_a n
• Second law (quotient law): The logarithm of fraction is equal to the difference between the logarithm of the numerator and the logarithm of the denominator. 
  log_a (m/n) = log_am - log_an
• Third law (power law): The logarithm of a power of a number is equal to the logarithm of the number multiplied by the power. 
  loga mⁿ = n log_a m