Assertion (A): log 2 = a and log 3 = b ⇒ 1 + log 12 = 2a + b Reason (R): 1 + log 12 = 1 + log 2 x 2 x 3 = 1 + 2log 2 + log 3 = 1 + 2a + b 1. A is true, but R is false. 2. A is false, but R is true. 3. Both A and R are true and R is the correct reason for A. 4. Both A and R are true and R is the incorrect reason for A.

Given, log 2 = a and log 3 = b ⇒ 1 + log 12 ⇒ 1 + log (4 x 3) ⇒ 1 + log (2 x 2 x 3) ⇒ 1 + log 4 + log 3 ⇒ 1 + log 22 + log 3 = 1 + 2log 2 + log 3 = 1 + 2a + b. ∴ A is false, but R is true. Hence, option 2 is the correct option.

Mathematics

Assertion (A): log 2 = a and log 3 = b
⇒ 1 + log 12 = 2a + b
Reason (R): 1 + log 12
= 1 + log 2 x 2 x 3
= 1 + 2log 2 + log 3
= 1 + 2a + b
A is true, but R is false.
A is false, but R is true.
Both A and R are true and R is the correct reason for A.
Both A and R are true and R is the incorrect reason for A.

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Given, log 2 = a and log 3 = b

⇒ 1 + log 12

⇒ 1 + log (4 x 3)

⇒ 1 + log (2 x 2 x 3)

⇒ 1 + log 4 + log 3

⇒ 1 + log 2² + log 3

= 1 + 2log 2 + log 3

= 1 + 2a + b.

∴ A is false, but R is true.

Hence, option 2 is the correct option.

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