document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=971225>Question 971225</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following logarithmic equation\r<BR>\n" );
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document.write( "log2(x-4)=4-log2(x+2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #593782 by </B><A HREF=/tutors/aboutme.mpl?userid=addingup><B>addingup(3677)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=addingup><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=addingup><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=593782\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (log(x-4))/(log(2)) = 4-(log(x+2))/(log(2))<BR>\n" );
document.write( "-4+(log(x-4))/(log(2))+(log(x+2))/(log(2)) = 0<BR>\n" );
document.write( "-(4 log(2)-log(x-4)-log(x+2))/(log(2)) = 0<BR>\n" );
document.write( "Multiply both sides by -log(2):<BR>\n" );
document.write( "4 log(2)-log(x-4)-log(x+2) = 0<BR>\n" );
document.write( "4 log(2)-log(x-4)-log(x+2) = log(16)+log(1/(x-4))+log(1/(x+2)) = log(16/((x-4) (x+2))):<BR>\n" );
document.write( "log(16/((x-4) (x+2))) = 0<BR>\n" );
document.write( "Take exp of both sides:<BR>\n" );
document.write( "16/((x-4) (x+2)) = 1<BR>\n" );
document.write( "Take the reciprocal of both sides:<BR>\n" );
document.write( "1/16 (x-4) (x+2) = 1<BR>\n" );
document.write( "Multiply both sides by 16:<BR>\n" );
document.write( "(x-4) (x+2) = 16<BR>\n" );
document.write( "Expand out terms on left:<BR>\n" );
document.write( "x^2-2 x-8 = 16<BR>\n" );
document.write( "Add 8 to both sides:<BR>\n" );
document.write( "x^2-2 x = 24<BR>\n" );
document.write( "Add 1 to both sides:<BR>\n" );
document.write( "x^2-2 x+1 = 25<BR>\n" );
document.write( "Write the left hand side as a square:<BR>\n" );
document.write( "(x-1)^2 = 25<BR>\n" );
document.write( "Take the square root of both sides:<BR>\n" );
document.write( "x-1 = 5 or x-1 = -5<BR>\n" );
document.write( "Add 1 to both sides:<BR>\n" );
document.write( "x = 6 or x-1 = -5<BR>\n" );
document.write( "Add 1 to both sides:<BR>\n" );
document.write( "x = 6 or x = -4<BR>\n" );
document.write( "(log(x-4))/(log(2)) => (log(-4-4))/(log(2))  =  (i pi+log(8))/(log(2)) ~~ 3.+4.53236 i<BR>\n" );
document.write( "4-(log(x+2))/(log(2)) => 4-(log(2-4))/(log(2))  =  (-i pi+3 log(2))/(log(2)) ~~ 3.-4.53236 i:<BR>\n" );
document.write( "So this solution is incorrect<BR>\n" );
document.write( "(log(x-4))/(log(2)) => (log(6-4))/(log(2))  =  1<BR>\n" );
document.write( "4-(log(x+2))/(log(2)) => 4-(log(2+6))/(log(2))  =  1:<BR>\n" );
document.write( "So this solution is correct<BR>\n" );
document.write( "Answer: x = 6 </SPAN>\n" );
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