document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1110101>Question 1110101</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Below is the graph of <BR>\n" );
document.write( "y=log2x<BR>\n" );
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document.write( "Translate it to become the graph of y=log2(x&#8722;4)+3<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #725113 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=725113\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> what you will find is:\r<BR>\n" );
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document.write( "log2(x-4) is the same as log2(x), but shifted to the right 4 units on a graph.\r<BR>\n" );
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document.write( "an example will show you what i mean.\r<BR>\n" );
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document.write( "when x = 6, the value of y = log2(x) is 2.585\r<BR>\n" );
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document.write( "when x = 10, the value of y = log2(x-4) is 5.585.\r<BR>\n" );
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document.write( "the value of y = log2(x-4) when x = 10 is the same value of y = log2(x) when x = 6, except that the value is 3 units higher.\r<BR>\n" );
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document.write( "how is this so?\r<BR>\n" );
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document.write( "well, when x = 6, y = log2(x) becomes log2(6) and, when x = 10, y = log2(x-4) becomes y = log2(10 - 6) which becomes log2(6).\r<BR>\n" );
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document.write( "the difference is the + 3 added to y = log2(x-4).\r<BR>\n" );
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document.write( "it raises the value of y + 3 units to make it y = 5.585, rather than y = 2.585.\r<BR>\n" );
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document.write( "here's what the graph of this example looks like.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/022103.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "this relationship happens with all equations, not just log equations.\r<BR>\n" );
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document.write( "here's a reference on transformation of algebraic equations.\r<BR>\n" );
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document.write( "those rules apply to log functions as well.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.mathsisfun.com/sets/function-transformations.html\" target = \"_blank\">https://www.mathsisfun.com/sets/function-transformations.html</a>\r<BR>\n" );
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