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.