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Find x satisfying the equation log^2(1 + 4/x) + log^2{1 - 4/(x + 4)}= 2log^2{2/(x-1) -1}

Find x satisfying the equation 


log^2(1 + 4/x) + log^2{1 - 4/(x + 4)}= 2log^2{2/(x-1) -1}

Grade:12

1 Answers

sanatan sharma
26 Points
9 years ago

log^2(1+4/x) + log^2(1-4(x+4)) = 2 log^2 (2/(x-1)-1)

log^2((x+4)/4) + log^2 (x/(x+4))  = 2 log^2 (2/(x-1)-1)

log^2 ((x+4)/4)(x/(x+4)) = 2 log^2 (2/(x-1)-1)

log^2 1 = 2 log^2 (2/(x-1)-1)

1 = (2/(x-1)-1)^2

± 1 = (2/(x-1)-1)

 x = 1 

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