Question

Assertion: If log 80 = a then `log 2 = (a - 1)/3`.

Reason: log 8 = 3 log 2.

विकल्प

• 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

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

Explanation:

We can write 80 as 80 = 8 × 10

So log 80 = log(8 × 10)

= log 8 + log 10 

Since log 10 = 1 base 10 log

We have a = log 80 = log 8 + 1

Using the reason log 8 = 3 log 2

Therefore, a = 3 log 2 + 1, which rearranged gives `log 2 = (a - 1)/3`

Hence, the reason is correct and it correctly explains the assertion.