Question

Assertion: If log 2 = a, log 3 = b then log 6 = ab.

Reason: log 6 = log 2 + log 3.

Options

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

A is false but R is true.

Explanation:

By logarithm properties,

log of a product equals the sum of logs: 

log(6) = log(2 × 3)

= log 2 + log 3

Since log 2 = a and log 3 = b, log 6 = a + b, not ab.

So, Assertion is false because it states log 6 = ab.

Reason is true because it correctly states the logarithm property log 6 = log 2 + log 3.