How Do You Calculate Log Base 3?

To calculate the logarithm base 3 of a number, you can use the change of base formula. The formula states:

• log_b(a) = log_c(a) / log_c(b)

Here, a is the number you want to find the log of, b is the base you are converting from (in this case, 3), and c is a new base you can choose, such as 10 or e (the natural logarithm base).

For example, to calculate log₃(9):

1. Choose a base (let’s use 10).
2. Use the change of base formula:
3. log₃(9) = log₁₀(9) / log₁₀(3)
4. On your calculator, find log₁₀(9) and log₁₀(3).
5. Calculate the values:
6. log₁₀(9) ≈ 0.9542 and log₁₀(3) ≈ 0.4771.
7. Now divide: 0.9542 / 0.4771 ≈ 2.

Thus, log₃(9) = 2 because 3² = 9.

This method works for any positive number to find its logarithm base 3, allowing you to easily calculate logs without a specific base feature on your calculator.