Question

Assertion: `2 log 3 - 1/2 log 4 + 3 log 2 = log 36`

Reason: `log a - log b + log c = log  a/(bc)`

पर्याय

• 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 true but R is false.

Explanation:

Assertion:

`2 log 3 - 1/2 log 4 + 3 log 2 = log 36` is true.

Proof: 2 log 3 = log3² = log 9

`1/2 log 4 = log 4^(1/2) = log 2`

3 log 2 = log 2³ = log 8

So the left side becomes log 9 – log 2 + log 8

= `log  (9 xx 8)/2`

= log 36, which proves the assertion true.

Reason:

`log a - log b + log c = log  a/(bc)` is false.

Because the correct log law is `log a - log b + log c = log ((a xx c)/b)`.

Therefore, Assertion is true, but Reason is false.