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Question

Solve the inequality: log3(x+2)(x+4)+log1/3(x+2)<12log37

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Solution

log3(x+2)(x+4)+log13(x+2)<12log37

log3(x+2)(x+4)log3(x+2)<22log37 (logabx=1blogax )

log3[(x+2)(x+4)x+2]<log37

x+4<7 (logax<logay;a>1x<y )

x<3 ...(1)

But log is defined when
x+2>0

x>2 ...(2)

(x+2)(x+4)>0

(,4)(2,) ...(3)

From (1), (2) and (3)

x(2,3)

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