If log log_{2} (5 + log_{3} a) = 3 and log_{5} (4a + 12 + log_{2} b) = 3, then a + b is equal to

- 67
- 40
- 32
- 59

### Answer

5 + log_{3} a = 2^{3} = 8

⇒ a = 27

Similarly,

4a + 12 + log_{2} b = 5^{3} = 125

Since a = 27,

4(27) + 12 + log_{2} b = 125

log_{2} b = 5

⇒ b = 2^{5} = 32

a + b = 27 + 32 = 59

**The correct option is D.**