Question

If Log (P) = (1/2) Log (Q) = (1/3) Log (R), then which of the following options is TRUE?
1. P² = Q³R²
2. Q² = PR
3. Q² = R³P
4. R = P²Q²

Answer 1

Correct Answer - Option 2 : Q² = PR

Explanation:

Let Log (P) = (1/2) Log (Q) = (1/3) Log (R) = l

∴ P = 10^k, Q = 10^2k, R = 10^3k

Now,

Option 1:

P²=Q³R²

(10^k)² = (10^2k)³ (10^3k)² 

10^2k ≠ 10^12k

Option 2:

Q² = PR

10^4k = (10^3k)(10^k)

10^4k = 10^4k

∴Q² = PR follows the given relation.

Option 3:

Q² = R³P ⇒ 10^2k ≠ 10^7k

Option 4:

R=P²Q² ⇒ 10^3k ≠ 10^6k

∴ Only option(2) is correct.