If f(x) = log₂(x), what is f(13)?

To find the value of f(13) where f(x) = log₂(x), we need to substitute x with 13. So, we are calculating:

f(13) = log₂(13)

The logarithm base 2 of a number tells us the power to which 2 must be raised to obtain that number. In this case, we want to find out what exponent y satisfies:

2^y = 13

We can use the change of base formula to compute log₂(13). The change of base formula states that:

log_b(a) = log_k(a) / log_k(b)

Using base 10 (common logarithm), we get:

log₂(13) = log₁₀(13) / log₁₀(2)

Approximate values of these logarithms can be calculated using a calculator:

• log₁₀(13) ≈ 1.1139
• log₁₀(2) ≈ 0.3010

Now, substituting these values into the change of base formula gives us:

log₂(13) ≈ 1.1139 / 0.3010 ≈ 3.70

Thus, the final answer is:

f(13) ≈ 3.70