Consider the following two statements :

Statement 1: log₅ 150 = log₅ 25 + log₅ 125

Statement 2: log_a (b + c) = log_a b + log_a c

Which of the following is valid?

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and Statement 2 is false.

4. Statement 1 is false, and Statement 2 is true.

According to statement 1; log₅ 150 = log₅ 25 + log₅ 125

Solving R.H.S.,

⇒ log₅ 25 + log₅ 125

⇒ log₅ (25 x 125)

⇒ log₅ 3125.

As, log₅ 150 ≠ log₅ 3125

∴ Statement 1 is false.

According to statement 2; log_a (b + c) = log_a b + log_a c

Solving R.H.S.

⇒ log_a b + log_a c

⇒ log_a (b x c)

⇒ log_a bc.

As, log_a (b + c) ≠ log_a bc

∴ Statement 2 is false.

∴ Both statements are false.

Hence, option 2 is the correct option.