document.write( "Question 256861: Log2x+log2(x+2)=log2(x+6) \n" ); document.write( "

Algebra.Com's Answer #188920 by CharlesG2(834) $\"\"$ $\"About$

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Log2x+log2(x+2)=log2(x+6)\r
\n" ); document.write( "\n" ); document.write( "log(2x)+log(2*(x+2))=log(2*(x+6))\r
\n" ); document.write( "\n" ); document.write( "logb (mn) --> b=base --> logb (mn) = logb (m) + logb (n)
\n" ); document.write( "in this problem's case the base b is 10\r
\n" ); document.write( "\n" ); document.write( "log(2x)+log(2*(x+2))=log(2*(x+6))
\n" ); document.write( "log(2x*2*(x+2))=log(2*(x+6))
\n" ); document.write( "log(4x*(x+2))=log(2*(x+6))
\n" ); document.write( "log(4x^2+8x)=log(2x+12)\r
\n" ); document.write( "\n" ); document.write( "4x^2+8x=2x+12
\n" ); document.write( "4x^2+6x-12=0
\n" ); document.write( "b^2-4*a*c=6^2-4*4*(-12) --> a=4,b=6,c=-12
\n" ); document.write( "36-16*(-12)
\n" ); document.write( "36-(-192)
\n" ); document.write( "36+192
\n" ); document.write( "228 \r
\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"x+=+%28-6+%2B-+sqrt%28+228+%29%29%2F8+\"$
\n" ); document.write( " $\"x+=+%28-6+%2B-+sqrt%28+228+%29%29%2F8+\"$
\n" ); document.write( "228=2*114=2*2*57
\n" ); document.write( " $\"x+=+%28-6+%2B-+2%2Asqrt%2857%29%29%2F8+\"$
\n" ); document.write( " $\"x+=+%28-3+%2B-+sqrt%2857%29%29%2F4+\"$ (took out 2/2)
\n" ); document.write( " $\"x+=+%28-3%2F4+%2B-+sqrt%2857%29%2F4%29+\"$
\n" ); document.write( " $\"x+=+%28-0.75+%2B-+1.887459%29+\"$ (rounded the root/4 to 6 places)
\n" ); document.write( "x1=1.137459
\n" ); document.write( "x2=-2.637459\r
\n" ); document.write( "\n" ); document.write( "but going back to Log2x+log2(x+2)=log2(x+6)
\n" ); document.write( "we can not use x2 since we can not take the log of a negative number
\n" ); document.write( "since logb y = x is same as b^x=y, you would be asking what to the what is a negative number\r
\n" ); document.write( "\n" ); document.write( "so x is x1 or 1.137459\r
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