Log Calculator

Free online log calculator to calculate logarithms with any base. Find log base 10, natural log, and custom base logarithms with step-by-step calculation.

Log Calculator

log
=
log2 loge log10
* Provide any two values to calculate the logarithm, "e" can be entered as input. E.g: 2e4, 6e-3, 1.35e7
A mathematical representation of a logarithm is as follows: logb a = c
This means that b c = a

Change of Base Formula Calculator

log
log2 loge log10
=

What is Logarithm ?

A logarithm, often referred to as a "log," is a mathematical function that helps you determine how many times you need to multiply a specific number (the base) by itself to obtain another number. In other words, it's the inverse operation of exponentiation. Logarithms are frequently used in mathematics, science, engineering, and other fields.

The basic form of a logarithm is expressed as:

logb (a) = c

  • [i]b[/i] is the base of the logarithm.
  • [i]a[/i] is the number for which you want to find the logarithm.
  • [i]c[/i] is the result, indicating how many times you must raise the base [i]b[/i] to get [i]a[/i].

Example:

If the base is 10 (this is the most common base and is called the common logarithm), the logarithm of the number 100 with base 10 is 2 because [strong]10[sup]2[/sup] = 100[/strong]. So, we have [strong]log [sub]10[/sub]100 = 2[/strong].

Logarithm rules

Product rule

logb(a × c) = logb(a) + logb(c)

Quotient rule

logb(
ac
) = logb(a) - logb(c)

Power rule

logb(ac) = c × logb(a)

Base switch rule

logb(c) =
1logc(b)

Change of base rule

logb(a) =
logc(a)logc(b)