Question

Evaluate log5(100) using the change-of-base formula.

Answer 1

To evaluate log5(100), use the change-of-base formula: log5(100) = log(100) / log(5). Calculate log(100) as 2, then divide by log(5) using a calculator, which yields an approximate result of 2.861.

Step-by-step explanation:

To evaluate log5(100) using the change-of-base formula, we first need to understand the formula itself. The change of base formula is given by logb(a) = logc(a) / logc(b), where 'a' is the value we're taking the logarithm of, 'b' is the original base, and 'c' is the new base we are changing to, typically base 'e' (natural logarithm ln) or base 10 (common logarithm log).

To calculate log5(100), we choose base 10 for convenience, which is widely available on calculators:

log5(100) = log(100) / log(5)

Step 1: Evaluate log(100), which is 2 because 102 = 100.

Step 2: Evaluate log(5), which will require a calculator, but as an example, if log(5) is 0.6990:

Step 3: Now, divide the first result by the second: 2 / 0.6990 ≈ 2.861, hence log5(100) ≈ 2.861.