Which of the following statements is not correct?

Step-by-Step Solution

To identify the incorrect statement, we must evaluate each option based on standard logarithmic rules.

1. Option A: log(base 10) 10 = 1

   • Evaluation: Correct. The logarithm of a base to itself is always 1, because 10^1 = 10.

2. Option B: log(2 + 3) = log(2 * 3)

   • Evaluation: Incorrect. The logarithm of a sum is not equal to the logarithm of a product. In fact, log(a + b) is generally not equal to log(a) + log(b). Here, log(5) does not equal log(6).

3. Option C: log(base 10) 1 = 0

   • Evaluation: Correct. The logarithm of 1 to any base is always 0, because any non-zero number raised to the power of 0 is 1 (e.g., 10^0 = 1).

4. Option D: log(1 + 2 + 3) = log 1 + log 2 + log 3

   • Evaluation: Correct in this specific instance. While log(x + y + z) is not equal to log(x) + log(y) + log(z) generally, it happens to hold true here because log(1 + 2 + 3) = log(6) and log(1) + log(2) + log(3) = log(1 * 2 * 3) = log(6).

Conclusion

The statement that is not correct is Option B, as the rule for logarithms states that the logarithm of a product is the sum of the logarithms (log(xy) = log(x) + log(y)), not that the logarithm of a sum equals the logarithm of a product.