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find the value of x if 3 log 2+1/3 log 27-log4=log x |
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Answer» The numbers log 2, log (2x − 1) and log (2x + 3) are in A.P. ∴log (2x−1)−log 2 = log (2x+3)−log (2x−1)⇒log (2x−12)=log (2x+32x−1)⇒2x−12=2x+32x−1⇒(2x−1)2=2(2x+3)⇒22x+1−2.2x=2.2x+6⇒22x−4.2x−5=0 Let 2x=y.⇒y2−4y−5=0⇒(y−5)(y+1)=0⇒y=5 or y=−1∴2x=5 or 2x=−1 (not possible)Taking log on both the sides, we get: log 2x=log5⇒xlog2=log5⇒x=log 5 log 2=log2 5⇒x=log2 5 |
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