Option 1 : 17/2

Reading Comprehension Vol 1

2483

12 Questions
36 Marks
20 Mins

**Calculation:**

log (3^{P }× 4^{Q} × 5^{R}) = [log (3^{2 }× 4^{5} × 5^{4}) + log (3^{4 }× 4^{5} × 5^{6}) + log (3^{3 }× 4^{6} × 5^{20}) + log (3^{5 }× 12^{2} × 5^{4})]/4

⇒ 4 log (3^{P }× 4^{Q} × 5^{R}) = log (3^{2 }× 4^{5} × 5^{4}) + log (3^{4 }× 4^{5} × 5^{6}) + log (3^{3 }× 4^{6} × 5^{20}) + log (3^{5 }× 12^{2} × 5^{4})

⇒ log (3^{4P }× 4^{4Q} × 5^{4R}) = log (3^{16 }× 4^{18} × 5^{34})

⇒ 4P = 16 and 4Q = 18

⇒ P = 4 and Q = 4.5

⇒ P + Q = 8.5

**∴ The required answer is 17/2**

__Key Points__

log x + log y = log (x × y)