To calculate the logarithm in base 2, you probably need a calculator. However, if you know the result of the natural logarithm or the base 10 logarithm of the same argument, you can follow these easy steps to find the result. For a number x:

1. Find the result of either log10(x) or ln(x).

2. Divide the result of the previous step by the corresponding value between:

   • log10(2) = 0.30103; or

   • ln(2) = 0.693147.

3. The result of the division is log2(x).

In a computer world, binary code is of essential importance: words, numbers, pictures, and everything else can be reduced to a string of 0s and 1s. Since the binary code uses only two digits, the number 2 appears consistently in computer science.

The widespread appearance of log2 in computer science has no strong mathematical reason (since logarithms can change base by multiplication) but can be useful. For example, using log2 to compute entropy allows us to obtain the result expressed in bits, which are the natural unit.

The logarithm in base 2 of 256 is 8. To find this result, consider the following formula:

2^x = 256

The logarithm corresponds to the following equation:

log2(256) = x

In this case, we can check the powers of 2 to see if we can find the value of x: 2⁰ = 1, 2¹ = 2, 2² = 4, …, 2⁷ = 128, and 2⁸ = 256.

Since we found the argument of our logarithm, we can write that:

log2(256) = 8.