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ICSE Class 9 Answered

Logx+12x-1+log2x-1x+1=2;find x
Asked by Sunita | 26 Jan, 2018, 02:22: PM
answered-by-expert Expert Answer
begin mathsize 16px style Log subscript straight x plus 1 end subscript space 2 straight x minus 1 space plus space log subscript 2 straight x minus 1 end subscript space straight x plus 1 space equals 2
fraction numerator 1 over denominator space log subscript 2 straight x minus 1 end subscript space straight x plus 1 end fraction plus log subscript 2 straight x minus 1 end subscript space straight x plus 1 equals 2 space space space space space space space space space space space space space space space space space space space space space space space space open parentheses log subscript straight a space straight b equals fraction numerator 1 over denominator log subscript straight b space straight a end fraction close parentheses
Put space log subscript 2 straight x minus 1 end subscript space straight x plus 1 equals straight m
1 over straight m plus straight m equals 2
1 plus straight m squared equals 2 straight m
straight m squared minus 2 straight m plus 1 equals 0
left parenthesis straight m minus 1 right parenthesis squared equals 0
straight m equals 1
space log subscript 2 straight x minus 1 end subscript space straight x plus 1 equals 1 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space
straight x plus 1 equals 2 straight x minus 1 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open parentheses space space log subscript straight a space straight b space equals straight m rightwards double arrow straight b equals straight a to the power of straight m close parentheses
1 plus 1 equals 2 straight x minus straight x
straight x equals 2
end style
Answered by Sneha shidid | 26 Jan, 2018, 02:51: PM
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