document.write( "Question 22743: What is the value of X in the equation: log $\"2\"$ (x+1) + log $\"2\"$ (x-5) = 4 THANK YOU VERY MUCH!!!!! \n" ); document.write( "

Algebra.Com's Answer #11184 by venugopalramana(3286) $\"\"$ $\"About$

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log $\"2\"$ (x+1) + log $\"2\"$ (x-5) = 4
\n" ); document.write( "USING THE FORMULA LOG A TO BASE X = LOG A/LOG X TO A COMMON BASE OR STANDARD BASE.HENCE WE HAVE
\n" ); document.write( "{LOG (X+1)/LOG 2} + {LOG (X-5)/LOG 2}=4
\n" ); document.write( "LOG(X+1)+LOG(X-5)=4*LOG 2=LOG 2^4=LOG 16 (SINCE LOG X^N=N*LOG X)
\n" ); document.write( "LOG(X+1)(X-5)=LOG 16 (SINCE LOG X + LOG Y =LOG(X*Y))
\n" ); document.write( "TAKING ANTILOGS
\n" ); document.write( "(X+1)(X-5)=16
\n" ); document.write( "X^2-5X+X-5=16
\n" ); document.write( "X^2-4X-5-16=0
\n" ); document.write( "X^2-7X+3X-21=0
\n" ); document.write( "X(X-7)+3(X-7)=0
\n" ); document.write( "(X-7)(X+3)=0
\n" ); document.write( "HENCE X=7 OR X=-3 AS X=-3 LEADS TO LOG OF NEGATIVE NUMBERS WHICH DO NOT EXIT , THE ANSWER IS X=7
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