Enter any number into the calculator below to determine the log base 2 of that number. To calculate the log of that number in any other base, simply enter that into the calculator below.

Log Base 2 Formula

The following formula is used by the calculator above to calculate the log of a number.

log base 2 formula

Log Base 2 Definition

Conceptually, the log of a number y with base b is equal to the exponential value the base needs to be raised to in order to equal y. In other words, if you have a problem, say log base 2 of 4, the answer is 2 because 2^2=4.

Log Example

Let’s take a look at a step-by-step example of how to calculate the log of a number with any base.

  1. First, the number that we are to take the log of must be determined, For this example we will say that number, y, is equal to 25.
  2. Next, the base of the log needs to be chosen. For this example, we will take a base of 5.
  3. Finally, we need to set up the equation above to solve for X. So the log base 5 of 25.
  4. The answer to this equation is 2 since 5^2=25. 2 is the number that 5 needs to be raised to in order to equal 25.


What is a logarithm?
A logarithm is a mathematical operation that determines how many times a number, called the base, must be multiplied by itself to reach another number. It is the inverse operation of exponentiation.

Why is the log base 2 particularly important in computer science?
Log base 2 is especially significant in computer science because computers operate on binary systems. Calculations involving log base 2 are frequent in algorithms, data structure analysis, and determining the efficiency of operations.

Can logarithms be calculated for negative numbers?
No, logarithms cannot be directly calculated for negative numbers in the real number system because there is no real number exponent that a positive base can be raised to produce a negative result. However, logarithms of negative numbers can be discussed within the context of complex numbers.

How does changing the base of a logarithm affect its value?
Changing the base of a logarithm alters its value according to the change of base formula. However, the relationship between the numbers remains consistent. The change of base formula allows you to convert a logarithm to any base you prefer, facilitating easier calculation or comparison.