Question: If 60^a=3, 60^b=5 then 12^{[1-a-b]/[2(1-b)]} = ?

A: 1
B: 2
C: 3
D: Root(5)

Ans: B
Solution: 60^a=3
So, a = log₆₀3
60^b=5
So, b = log₆₀5

Now,
Let Y = 12^{[1-a-b]/[2(1-b)]}
Taking log with base 60 on both sides,
log₆₀Y=log₆₀12^{[1-a-b]/[2(1-b)]}
Or, log₆₀Y=[1-a-b]/[2(1-b)] log₆₀12

(1-a-b)/2(1-b) = (1- log₆₀3 - log₆₀5)/2(1 - log₆₀5)
                       = ( log₆₀60 - log₆₀3 - log₆₀5)/2(log₆₀60 - log₆₀5)
                       = [log₆₀(60/15)]/2[log₆₀(60/5)]
                       = log₆₀4/2log₆₀12
log₆₀Y = (log₆₀4/2log₆₀12)* log₆₀12
           = 1/2log₆₀4
            =log₆₀2
So, Y = 2 Ans