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solve for x: log 1/3 (x-1) + log 1/3 (x+1) + log √3 (5-x) plz helpppp.....

solve for x:


log1/3(x-1) + log1/3(x+1) + log√3(5-x) < 1


plz helpppp.....

Grade:11

1 Answers

vikas askiitian expert
509 Points
10 years ago

logax = logx/loga                 (property)

logxb = blogx                       (property)

log1/3(x-1) + log1/3(x+1) + log (5-x) < 1


logx-1/log1/3  + logx+1/log1/3 + log5-x/log√3 <1

 

-logx-1/log3  - logx+1/log3 + 2log5-x/log3 <1

-logx-1 - logx+1 + 2log5-x < log3                       (logab = loga + logb)

 2log5-x - logx2-1 < log3

 2log5-x < log3 + logx2-1

 2log5-x < log3(x2-1)

   (5-x)2 < 3(x2-1)

   now solve this & get the ans

 

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