document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1032364>Question 1032364</A>: <I><SPAN STYLE=\"word-break: break-all;\">  With reference to the fact that the functions log2 x and 2^x undo each other, explain each of the<BR>\n" );
document.write( "following statements.<BR>\n" );
document.write( "(a) log2 0 is undefined.<BR>\n" );
document.write( "(b) log2 x is negative when x is between 0 and 1.<BR>\n" );
document.write( "(c) log2 500 is between 8 and 9.<BR>\n" );
document.write( "(d) An x can be found so that log2(x) is greater than 1, 000, 000.\r<BR>\n" );
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document.write( "in all the log2 above 2 is the power of the log . I couldn't find a way to put the correct form in here. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #647015 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=647015\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C0%29 ALIGN=MIDDLE  ALT=\"log%282%2C0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is undefined because there is NO real number x such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ex+=+0 ALIGN=MIDDLE  ALT=\"2%5Ex+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "(b)  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%282%2C+x%29 ALIGN=MIDDLE  ALT=\"+log%282%2C+x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is negative when x is between 0 and 1 because, if you will notice the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%5Ex ALIGN=MIDDLE  ALT=\"y=2%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >, for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%3C+y=2%5Ex+%3C1 ALIGN=MIDDLE  ALT=\"0+%3C+y=2%5Ex+%3C1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the corresponding set of pullback x-values is exactly the interval (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 0).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+2%5Ex%29 ALIGN=MIDDLE  ALT=\"graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+2%5Ex%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(c)  This is easy, because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E8+=256+%3C+500+%3C+2%5E9=512 ALIGN=MIDDLE  ALT=\"2%5E8+=256+%3C+500+%3C+2%5E9=512\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "(d)  An x can be found so that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Cx%29 ALIGN=MIDDLE  ALT=\"log%282%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is greater than 1,000,000.  Indeed, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E20+ ALIGN=MIDDLE  ALT=\"2%5E20+\"   DISABLED_style= \"max-width:90%; height:auto;\" > =  1,048,576 > 1,000,000.\r<BR>\n" );
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document.write( "You have to remember that logarithm is just a fancy way of writing an exponent satisfying a base condition. </SPAN>\n" );
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