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Solve log(3)(x+2)(x+4)+log(1//3)(x+2) l...

Solve ` log_(3)(x+2)(x+4)+log_(1//3)(x+2) lt 1/2 log_(sqrt3)7`.

Text Solution

Verified by Experts

The correct Answer is:
`x in (-2, 3)`
`(x+2)(x+4) gt 0, x+2 gt 0`
`rArr x gt -2`
Given inequality is
` log_(3)(x+2)(x+4)- log_(3) (x+2) lt((log 7)//2)/((log 3)//2)`
`rArr log_(3)(x+4) lt log_(3) 7`
` rArr x+ 4 lt 7 or x lt 3`
` rArr x in (-2, 3)`
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