document.write( "Question 52368: solve for x\r
\n" ); document.write( "\n" ); document.write( "log base 2x + log base 2(x-6)=4\r
\n" ); document.write( "\n" ); document.write( "my answer was x=2\r
\n" ); document.write( "\n" ); document.write( "am I correct? \n" ); document.write( "
Algebra.Com's Answer #34894 by funmath(2933)\"\" \"About 
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I am having a little difficulty interpretting this, but if I understand what you have typed in, your answer is not right.
\n" ); document.write( "log base 2 (x)+log base 2 (x-6)=4
\n" ); document.write( "log base 2 ((x)(x-6))=4
\n" ); document.write( "(x)(x-6)=2^4
\n" ); document.write( "x^2-6x=16
\n" ); document.write( "x^2-6x-16=16-16
\n" ); document.write( "x^2-6x-16=0
\n" ); document.write( "(x-8)(x+2)=0
\n" ); document.write( "x-8=0
\n" ); document.write( "x-8+8=0+8
\n" ); document.write( "x=8
\n" ); document.write( "x+2=0
\n" ); document.write( "x+2-2=0-2
\n" ); document.write( "x=-2
\n" ); document.write( "With logs, you have to check for extraneous (false) solutions. Substitute your answers back into the original equation and see if they are true.
\n" ); document.write( "For x=8
\n" ); document.write( "log base 2 (8)+ log base 2(8-6)=4
\n" ); document.write( "log base 2(2^3)+log base 2(2)=4
\n" ); document.write( "3+1=4
\n" ); document.write( "so x=8 is a solution
\n" ); document.write( "for -2, log base 2 (-2) shows that x=-2 is extraneous because you can't take the log of a negative number.
\n" ); document.write( "Therefore, the only answer is x=8. \n" ); document.write( "
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