document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=427022>Question 427022</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have been reading and trying very hard to get these logarithms, they just make my head spin. I am starting to kind of get the basics, but the book my school uses does not explain things clearly. How would one go about graphing these? Please show all steps so I can try to understand this process from start to finish.\r<BR>\n" );
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document.write( "A)  y=1/2e^x-1\r<BR>\n" );
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document.write( "B)   y= -3 log 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 #297356 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=297356\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I have been reading and trying very hard to get these logarithms, they just make my head spin. I am starting to kind of get the basics, but the book my school uses does not explain things clearly. How would one go about graphing these? Please show all steps so I can try to understand this process from start to finish. <BR>\n" );
document.write( "A) y=1/2e^x-1 <BR>\n" );
document.write( "B) y= -3 log x + 2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Let us take the first equation, y=1/2e^x-1<BR>\n" );
document.write( "Let us break it into its parts.<BR>\n" );
document.write( "First, let y=1/e^x<BR>\n" );
document.write( "You can see that when x=0, y=1.<BR>\n" );
document.write( "This will be true no matter what the base is.<BR>\n" );
document.write( "You can also see that as x becomes very large, y approaches zero but does not reach zero. This makes the x-axis an asymptote.<BR>\n" );
document.write( "Now we have two things to graph the equation, the point (0,1) and the x-axis as the asymptote.<BR>\n" );
document.write( "What happens to the curve when x<0?<BR>\n" );
document.write( "The equation will now change from 1/e^-x to e^x.  As you can see as x becomes more negative, e^x becomes larger and larger to infinity. So now you should have enough information to graph 1/e^x. But wait we want to graph 1/2e^x-1. No sweat, all we need is a little more algebra. The 2 in the denominator changes the y-intercept from (0,1) to (0,1/2) and makes the curve steeper.  The -1 just bumps the entire curve down one unit. This  changes the asymptote to y=-1 instead of the x-axis.<BR>\n" );
document.write( "That is all there is to it.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Let us try the second equation, y= -3 log x + 2<BR>\n" );
document.write( "first change -3logx to logx^-3 or log 1/x^3<BR>\n" );
document.write( "When x=1,log 1/x^3=log 1/1=log1=0 (Log 1 of any base =0)<BR>\n" );
document.write( "So you have this point to graph, (1,0)<BR>\n" );
document.write( "As x becomes less than 1, 1/x^3 increases rapidly approaching the y-axis but does not cross the y-axis because there is no such thing as the log of a negative number. So the y-axis becomes an asymptote for the graph.  As x becomes greater than 1, you are not taking the logarithim of a fraction which gives you a negative number, so y will become increasingly negative but not as rapidly. The+2 will just bump the entire curve up 2 points.<BR>\n" );
document.write( "Hope this helps!<BR>\n" );
document.write( "See the graph of the first equation below: The second equation will not graph with this format.\r<BR>\n" );
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document.write( "..<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+1%2F2e%5Ex-1%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+1%2F2e%5Ex-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "  </SPAN>\n" );
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