Question

Assertion: If log 5 = m, then log 500 = 100 + m

Reason: log ab = log a + log b

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:

Assertion (A) states: If log 5 = m, then log 500 = 100 + m.

This is false because log 500 is log (5 × 100)

= log 5 + log 100

= m + 2, not 100 + m

The value 100 + m is incorrect because the logarithm of 100 is 2, not 100.

Reason (R) states: log(ab) = log a + log b.

This is a true and fundamental logarithmic identity.

Therefore, while the reason is true, it is not the correct explanation for the asserted relation in (A), which is itself false.