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If (log)(12)27=a , then find (log)6 16in...

If `(log)_(12)27=a ,` then find `(log)_6 16int e r m sofa`

Text Solution

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Since `a= log_(12) 27 = log_(12)(3)^(3) = 3 log_(12) 3`,
` = 3/(log_(3) 12) = 3/(1+log_(3) 4) = 3/(1+2log_(3) 2)`
` :. log_(3) 2 = (3-a)/(2a)`
Then, `log_(6) 16 = log_(6) 2^(4) = 4 log_(6) 2 = 4/(log_(2) 6)`
` = 1/(1+log_(2)3) = 4/(1+(2a)/(3-a)) = 4 ((3-a)/(3+a))`
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