This cheat sheet covers the high school math concept – Logarithm.


This concept is one of the important tools in Algebra as well as Calculus. The logarithm of a given number N is defined as the power to which another number a (called the base) must be raised, to give that number N. For example, the log of 1000 to the base 10 is 3, because 10 must be raised to the power 3 to give 1000. The logarithm of N to the base a is denoted as loga (N) or logaN.

The logarithm function is quite an important function and occurs in many real-life situations. It is closely related to the exponential function. Infact, y = log(x) is the inverse function of the exponential function, y = ex. The base in log(x) is assumed to be e, unless specified otherwise.

This one page PDF covers summarised theory and the most important formulas related to the concept. Keep it handy while you’re revising the concept, especially before an exam.

The topics included in this cheat sheet are:

  • Definition
  • Properties
  • Sum of Logarithms
  • Difference of Logarithms
  • Logarithm of the Power of a Number
  • Logarithm of 1
  • Base Change Formula
  • Inequalities involving Logarithm
  • Graph of Log(x)

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