Given log (x + 4) = log(4) + log(x)
⇒ x + 4 = 4x
∴ x = 4/3

Similarly y = 5/4

Correct Option: C

Given log (x + 4) = log(4) + log(x)
⇒ x + 4 = 4x
∴ x = 4/3

Similarly y = 5/4

∴ x > y

Given log( x - 5) = log(x) - log(5)
⇒ x -5 = x/5
∴ x = 25/ 4 ....(i)

Again from question
log(y - 6) = log(y) - log(6)
⇒ y - 6 = y/6
∴ y = 36/5 ...(ii)

Correct Option: B

Given log( x - 5) = log(x) - log(5)
⇒ x -5 = x/5
∴ x = 25/ 4 ....(i)

Again from question
log(y - 6) = log(y) - log(6)
⇒ y - 6 = y/6
∴ y = 36/5 ...(ii)

From equations (i) & (ii) x < y

8⁵⁷ = (2³)⁵⁷ = 2¹⁷¹
∴ Required answer = (171 log₁₀ 2 + 1 )

Correct Option: A

8⁵⁷ = (2³)⁵⁷ = 2¹⁷¹
∴ Required answer = (171 log₁₀ 2 + 1 )
= [171 x 0.3010] + 1 = [51.4710] +1
= 51+1 =52

8¹⁰ = (2³)¹⁰
∴ Required answer = [30 log₁₀ 2 + 1]

Correct Option: D

8¹⁰ = (2³)¹⁰
∴ Required answer = [30 log₁₀ 2 + 1]
= [30 x 0.3010] + 1
= 9.03 + 1
= 9 + 1
= 10