document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1081007>Question 1081007</A>: <I><SPAN STYLE=\"word-break: break-all;\"> graph y=-log2(x)\r<BR>\n" );
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document.write( "with showing order pair solution </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #695070 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=695070\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> using the desmos.com calculator, you can graph this equation as follows:\r<BR>\n" );
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document.write( "y = log2(x)\r<BR>\n" );
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document.write( "y = log(x) / log(2)\r<BR>\n" );
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document.write( "x = 2^(-y)\r<BR>\n" );
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document.write( "all 3 equations will create the identical graph.\r<BR>\n" );
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document.write( "this is because:\r<BR>\n" );
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document.write( "the log conversion formula says that log2(x) = log(x) / log(2)\r<BR>\n" );
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document.write( "the basic definition of logs says that y = log2(x) if and only if 2^y = x\r<BR>\n" );
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document.write( "your equation is y = -log2(x)\r<BR>\n" );
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document.write( "the base conversion formula becomes y = -log(x) / log(2).\r<BR>\n" );
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document.write( "the basic definition of logs says that y = log2(x) if and only if 2^y = x.\r<BR>\n" );
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document.write( "but your equation is y = -log2(x)\r<BR>\n" );
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document.write( "multiply both sides of this equation by -1 and you get:\r<BR>\n" );
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document.write( "-y = log2(x)\r<BR>\n" );
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document.write( "now use the basic definition to get -y = log2(x) if and only if 2^(-y) = x\r<BR>\n" );
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document.write( "this is the same as x = 2^-y which was graphed.\r<BR>\n" );
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document.write( "the alternative way to derive this is a little more convoluted but gets you the same equivalence.\r<BR>\n" );
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document.write( "start with y = -log2(x)\r<BR>\n" );
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document.write( "by the rules of logs, this is equivalent to y = -1 * log2(x) which is the same as y = log2(x^-1)\r<BR>\n" );
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document.write( "by the basic definition of logs, this is true if and only if 2^y = x^-1\r<BR>\n" );
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document.write( "since x^-1 is the same as 1/x, this becomes 2^y = 1/x\r<BR>\n" );
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document.write( "since 2^y is the same as 1/(2^-y), this becomes 1/(2^-y) = 1/x\r<BR>\n" );
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document.write( "this is true if and only if 2^-y = x which is the same as x = 2^-y\r<BR>\n" );
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document.write( "the graph is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/051304.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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