document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=251254>Question 251254</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Evaluate the logarithmic equation for three values of x that are greater than 1, three values of x that are between 0 and 1, and at x=1. Show your work. Use the resulting ordered pairs to plot the graph; submit the graph via the Dropbox. State the equation of the line asymptotic to the graph (if any).\r<BR>\n" );
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document.write( "y = log4 (x) + 4<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 #182960 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=182960\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+log%284%2C+%28x%29%29+%2B+4 ALIGN=MIDDLE  ALT=\"y+=+log%284%2C+%28x%29%29+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since the logarithm is base 4 ans since no calculator I know can find base 4 logarithms, it will help tremendously if we choose our x values wisely. We want to choose x's that are powers of 4! For the three x's greater than 1: 4, 16 and 64 (since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+=+4%5E1 ALIGN=MIDDLE  ALT=\"4+=+4%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16+=+4%5E2 ALIGN=MIDDLE  ALT=\"16+=+4%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64+=+4%5E3 ALIGN=MIDDLE  ALT=\"64+=+4%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >). For the x's between 0 an 1: 1/4, 1/16 and 1/64 (since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4+=+4%5E%28-1%29 ALIGN=MIDDLE  ALT=\"1%2F4+=+4%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F16+=+4%5E%28-2%29 ALIGN=MIDDLE  ALT=\"1%2F16+=+4%5E%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F64+=+4%5E%28-3%29 ALIGN=MIDDLE  ALT=\"1%2F64+=+4%5E%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. And even x = 1 is a power of 4 since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+=+4%5E0 ALIGN=MIDDLE  ALT=\"1+=+4%5E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >!<br><BR>\n" );
document.write( "Using these x's we get:<BR>\n" );
document.write( "x = 4: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+log%284%2C+%284%29%29+%2B+4+=+1+%2B+4+=+5 ALIGN=MIDDLE  ALT=\"y+=+log%284%2C+%284%29%29+%2B+4+=+1+%2B+4+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 16: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+log%284%2C+%2816%29%29+%2B+4+=+2+%2B+4+=+6 ALIGN=MIDDLE  ALT=\"y+=+log%284%2C+%2816%29%29+%2B+4+=+2+%2B+4+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 64: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+log%284%2C+%2864%29%29+%2B+4+=+3+%2B+4+=+7 ALIGN=MIDDLE  ALT=\"y+=+log%284%2C+%2864%29%29+%2B+4+=+3+%2B+4+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 1/4: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+log%284%2C+%281%2F4%29%29+%2B+4+=+-1+%2B+4+=+3 ALIGN=MIDDLE  ALT=\"y+=+log%284%2C+%281%2F4%29%29+%2B+4+=+-1+%2B+4+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 1/16: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+log%284%2C+%281%2F16%29%29+%2B+4+=+-2+%2B+4+=+2 ALIGN=MIDDLE  ALT=\"y+=+log%284%2C+%281%2F16%29%29+%2B+4+=+-2+%2B+4+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 1/64: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+log%284%2C+%281%2F64%29%29+%2B+4+=+-3+%2B+4+=+1 ALIGN=MIDDLE  ALT=\"y+=+log%284%2C+%281%2F64%29%29+%2B+4+=+-3+%2B+4+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+log%284%2C+%281%29%29+%2B+4+=+0+%2B+4+=+4 ALIGN=MIDDLE  ALT=\"y+=+log%284%2C+%281%29%29+%2B+4+=+0+%2B+4+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We now have 7 points to plot.<br><BR>\n" );
document.write( "The asymptotes for a logarithmic equation will be vertical asymptotes at values for x that make an argument of a logarithm zero, if any. We have just one logarithm so we find the asymptotes, if any, by setting the argument equal to zero and solving:<BR>\n" );
document.write( "x = 0<BR>\n" );
document.write( "(Not much solving to do here!) There is a vertical asymptote at x = 0 (aka the y-axis). </SPAN>\n" );
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