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).

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.

The difference between ln and log2 is the base. The logarithm is the inverse operation of exponentiation, that is, the power of a number, and it answers the question: "what is the exponent that produces a given result?".

The base of the logarithm is the number to which you apply the exponent: in the case of ln, the number is e, Neper's number. For log2, you must consider the number 2. To sum up:

• If b = ln(x), then e^b = x; and
• If c = log2(x), then 2^c = x.