Which of the following statements about common logarithms (base 10) is not correct?

Introduction / Context:
This conceptual question checks whether students understand the basic properties of common logarithms and know when addition inside a log can or cannot be simplified. Many errors in log problems come from misusing sum and product rules, so identifying the incorrect statement is an important skill. All logs here are common logs, that is logarithms to base 10.

Given Data / Assumptions:
We are given four statements:
- A: log 10 = 1.
- B: log (2 + 3) = log (2 x 3).
- C: log 1 = 0.
- D: log (1 + 2 + 3) = log 1 + log 2 + log 3.
All logs are base 10, and we must identify which statement is not correct.

Concept / Approach:
The key log properties are:
1. log 10 = 1 because 10^1 = 10.
2. log 1 = 0 because 10^0 = 1.
3. log (A B) = log A + log B, but log (A + B) is not equal to log A + log B in general.
We evaluate each option using these rules. We check whether each side represents the same quantity. If any equality incorrectly treats a sum as if it were a product, that statement is invalid.

Step-by-Step Solution:
Check option A: log 10 = 1. Since 10^1 = 10, this is correct. Check option C: log 1 = 0. Since 10^0 = 1, this is also correct. Check option B: log (2 + 3) = log (2 x 3). Left side is log 5 and right side is log 6. Because 5 is not equal to 6, log 5 is not equal to log 6, so option B is incorrect. Check option D: log (1 + 2 + 3) = log 1 + log 2 + log 3. Left side is log 6. Right side is log 1 + log 2 + log 3 = 0 + log 2 + log 3 = log (2 x 3) = log 6, using the product rule. Therefore option D is correct because both sides equal log 6.

Verification / Alternative check:
Numerically, we can approximate the logs. Using base 10, log 5 is about 0.6990, while log 6 is about 0.7782. Clearly these are not equal, which confirms that log (2 + 3) is not equal to log (2 x 3). For statement D, log 2 is about 0.3010 and log 3 is about 0.4771, so log 2 + log 3 is about 0.7781, which matches log 6 up to rounding. This confirms that option D is correct, whereas option B is not.

Why Other Options Are Wrong:
The question asks for the statement that is not correct, so only option B is wrong.
- Option A is consistent with the fundamental definition of the common logarithm of 10.
- Option C is consistent with the fundamental definition of the common logarithm of 1.
- Option D correctly uses the product rule, because 1 x 2 x 3 equals 6, and the log of the product equals the sum of the logs.

Common Pitfalls:
A very common mistake is to treat log (A + B) as log A + log B, which is never generally true. This leads to errors in many algebraic and aptitude problems. Another pitfall is not recognising that log (1 + 2 + 3) is log 6, and that log 1 + log 2 + log 3 simplifies to log 6 via the product rule. Students may also assume that any equality involving logs is correct if the numbers look small and simple. It is crucial to remember exactly when the log of a product equals the sum of logs and that there is no simple rule for the log of a sum.

Final Answer:
The statement that is not correct is log (2 + 3) = log (2 x 3).