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Solve : 3logx(4)+ 2log(4x)4+3log(16x)4=0...

Solve : `3log_x(4)+ 2log_(4x)4+3log_(16x)4=0`

Text Solution

Verified by Experts

The correct Answer is:
` x = 1/2, 1/8`
`3log_(x) 4+2 log_(4x)4+3log_(16x) 4 =0`
` or 3/(log_(4)x)+2/(log_(4)4x) + 3/(log_(4) 16x) =0`
`or 3/(log_(4) x) + 2/(1+log_(4)x) + 3/(2+log_(4) x) =0`
` or 3/y + 2/(1+y) +3/(2+y) =0" "("putting y " log_(4) x)`
` or 4y^(2)+8y+3 = 0`
` or (2y+3)(2y+1) =0`
` or y = (-1)/2,(-3)/2`
` :. x = 1/2 , 1/8`
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