How Do You Convert Log Base 2 to Log Base 10?

To convert a logarithm from base 2 to base 10, you can use the change of base formula. The formula is:

log₁₀(x) = log₂(x) / log₂(10)

Here’s a step-by-step explanation:

1. Identify the value: Let’s say you have a logarithm in base 2, such as log₂(x).
2. Apply the change of base formula: Use the formula log₁₀(x) = log₂(x) / log₂(10).
3. Calculate log₂(10): The value of log₂(10) is approximately 3.3219.
4. Divide: Divide log₂(x) by 3.3219 to get log₁₀(x).

For example, if you want to convert log₂(8) to base 10:

log₂(8) = 3 (since 2³ = 8).

Using the formula:

log₁₀(8) = 3 / 3.3219 ≈ 0.9031.

So, log₁₀(8) ≈ 0.9031.