SOLUTION: What is the value of X in the equation: log{{{2}}}(x+1) + log{{{2}}}(x-5) = 4 THANK YOU VERY MUCH!!!!!

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: What is the value of X in the equation: log{{{2}}}(x+1) + log{{{2}}}(x-5) = 4 THANK YOU VERY MUCH!!!!!      Log On

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 Algebra: Logarithm Solvers Lessons Answers archive Quiz In Depth

 Question 22743: What is the value of X in the equation: log(x+1) + log(x-5) = 4 THANK YOU VERY MUCH!!!!!Answer by venugopalramana(3286)   (Show Source): You can put this solution on YOUR website!log(x+1) + log(x-5) = 4 USING THE FORMULA LOG A TO BASE X = LOG A/LOG X TO A COMMON BASE OR STANDARD BASE.HENCE WE HAVE {LOG (X+1)/LOG 2} + {LOG (X-5)/LOG 2}=4 LOG(X+1)+LOG(X-5)=4*LOG 2=LOG 2^4=LOG 16 (SINCE LOG X^N=N*LOG X) LOG(X+1)(X-5)=LOG 16 (SINCE LOG X + LOG Y =LOG(X*Y)) TAKING ANTILOGS (X+1)(X-5)=16 X^2-5X+X-5=16 X^2-4X-5-16=0 X^2-7X+3X-21=0 X(X-7)+3(X-7)=0 (X-7)(X+3)=0 HENCE X=7 OR X=-3 AS X=-3 LEADS TO LOG OF NEGATIVE NUMBERS WHICH DO NOT EXIT , THE ANSWER IS X=7