If log log2 (5 + log3 a) = 3 and log5 (4a + 12 + log2 b) = 3

• Logarithms

If log log₂ (5 + log₃ a) = 3 and log₅ (4a + 12 + log₂ b) = 3, then a + b is equal to

1. 67
2. 40
3. 32
4. 59

Answer

5 + log₃ a = 2³ = 8

⇒ a = 27

Similarly,

4a + 12 + log₂ b = 5³ = 125

Since a = 27,

4(27) + 12 + log₂ b = 125

log₂ b = 5

⇒ b = 2⁵ = 32

a + b = 27 + 32 = 59

The correct option is D.