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Let a,bepsilonR^+ for which 60^a=3 and 6...

Let `a,bepsilonR^+` for which `60^a=3` and `60^b=5` then `12^((1-a-b)/(2(1-b)))` is equal to

Text Solution

Verified by Experts

The correct Answer is:
`2`
`60^(a) = 3 rArr a = log_(60)3`
`60^(b) = 5 rArr b = b = log_(60)5`
`(1 - a - b)/(2(1 - b)) = (1 - log_(60) 3 - log_(60) 5)/(2(1 - log_(60)5)) = log_(60)((60)/(3 xx 5))/(2log_(60)((60)/(5)))`
`(log_(60)(4))/(2log_(60)(12)) = (log_(60)2)/(log_(60)12) = log_(12)2`
`:. (12)^(log_(12)2 = 2`
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