What is the value of f(12) for the function f(x) = log₅(x + 1)?

To find the value of f(12) for the function f(x) = log₅(x + 1), we will substitute 12 into the function.

First, we will calculate x + 1 when x = 12:

• 12 + 1 = 13

Next, we need to find f(12) = log₅(13). This means we need the base 5 logarithm of 13.

The change of base formula for logarithms is:

• logₐ(b) = log(c) / log(a) where c could be any base, commonly base 10 or base e.

Using base 10 (common logarithm), we calculate:

• f(12) = log₅(13) = log(13) / log(5)

If we calculate these values (using a calculator):

• log(13) ≈ 1.113943
• log(5) ≈ 0.6990

Now, we can evaluate:

• f(12) ≈ 1.113943 / 0.6990 ≈ 1.594534

Thus, the value of f(12) for the function f(x) = log₅(x + 1) is approximately 1.5945.