Assertion (A): log_x (m x n x p) = log_x m + log_x n + log p.

Reason (R): The logarithm of a product at any non-zero base is equal to the sum of the logarithms of its factors at the same base.

1. A is true, R is false.
2. A is false, R is true.
3. Both A and R are true.
4. Both A and R are false.

A is false, R is true.

Explanation

Given,

log_x (m x n x p) = log_x m + log_x n + log p

The product law of logarithms states that :

log_a (b x c) = log_a b + log_a c

So, log_x (m x n x p) = log_x m + log_x n + log_x p

≠ log_x m + log_x n + log p

∴ Assertion (A) is false.

The logarithm of a product at any non-zero base is equal to the sum of the logarithms of its factors at the same base.

i.e., log_a (b x c) = log_a b + log_a c

∴ Reason (R) is true.

Hence, Assertion (A) is false, Reason (R) is true.