Quantitative Aptitude – Algebra – Logarithms – If log(base2)(5 + log(base3) a)

Slot -1 – Quantitative Aptitude – Algebra – Logarithms – If log(base2)(5 + log(base3) a) 

If log₂(5 + log₃a) = 3 and log₅(4a + 12 + log₂ b) = 3, then a + b is equal to?

a) 59

b) 40

c) 67

d) 32

Solution:

Given, log₂(5 + log₃ a) = 3

5 + log₃ a = 2^3 = 8

log₃ a = 3

so a =  3^3 = 27

Now log(base5⁡) (4a+12+log(base2)⁡ b)=3

Or 4a + 12 + log(base2) b) = 125

log(base2)⁡ b = 125-12-4×27=5

So b = 2^5 = 32

Thus a+b = 59

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