document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=211361>Question 211361</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I desperately need help.  I have a 60 average right now and 2 weeks left.  Please help me understand what I need to do.  I have 2 weeks left to pass this class. \r<BR>\n" );
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document.write( "Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Show your work. Use the resulting ordered pairs to plot the graph; State the equation of the line asymptotic to the graph.\r<BR>\n" );
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document.write( "1. y= 5^x\r<BR>\n" );
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document.write( "2. y= log 7 ^x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #159793 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=159793\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Show your work. Use the resulting ordered pairs to plot the graph; State the equation of the line asymptotic to the graph.\r<BR>\n" );
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document.write( "1. y= 5^x\r<BR>\n" );
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document.write( "2. y= log 7 ^x<BR>\n" );
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document.write( "PROBLEM NUMBER 1<BR>\n" );
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document.write( "y = 5^x<BR>\n" );
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document.write( "let x = -5, -3, -1, 0, 1, 3, 5<BR>\n" );
document.write( "when x = -5, y = 5^(-5) = .00032<BR>\n" );
document.write( "when x = -3, y = 5^(-3) = .008<BR>\n" );
document.write( "when x = -1, y = 5^(-1) = .2<BR>\n" );
document.write( "when x = 0, y = 5^0 = 1<BR>\n" );
document.write( "when x = 1, y = 5^1 = 5<BR>\n" );
document.write( "when x = 3, y = 5^3 = 5*5*5 = 125<BR>\n" );
document.write( "when x = 5, y = 5^5 = 5*5*5*5*5 = 3125<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you find the x value of each pair and then the y value of each pair and you place your point on the intersection of the x value and y value.<BR>\n" );
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document.write( "you do this for each coordinate pair in turn.<BR>\n" );
document.write( "a coordinate pair would be an x value with its corresponding y value.<BR>\n" );
document.write( "example:<BR>\n" );
document.write( "when x = 3, y = 125<BR>\n" );
document.write( "your coordinate pair is (3,125)<BR>\n" );
document.write( "when x = -3, y = .008<BR>\n" );
document.write( "your coordinate pair is (-3,.008)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your graph will look like this:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-8%2C%2B8%2C-5000%2C5000%2C5%5Ex%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-8%2C%2B8%2C-5000%2C5000%2C5%5Ex%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This graph has an asymptote at y = 0<BR>\n" );
document.write( "as x gets more negative, y approaches 0 but never quite makes it.<BR>\n" );
document.write( "when x = -10, y = 1.024 * 10^-7<BR>\n" );
document.write( "when x = -100, y = 1.2676506 * 10^-70<BR>\n" );
document.write( "y will approach 0 but never reaches 0 making y = 0 an asymptote of this equation.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "PROBLEM NUMBER 2<BR>\n" );
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document.write( "y = log(7^x)<BR>\n" );
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document.write( "This is the same as x * log(7) by one of the laws of logarithms that you would need to know.<BR>\n" );
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document.write( "let x = -5, -3, -1, 0, 1, 3, 5 again.<BR>\n" );
document.write( "when x = -5, y = -5*log(7) = -4.2254902<BR>\n" );
document.write( "when x = -3, y = -3*log(7) = -2.53529412<BR>\n" );
document.write( "when x = -1, y = -1*log(7) = -.84509804<BR>\n" );
document.write( "when x = 0, y = 0*log(7) = 0<BR>\n" );
document.write( "when x = 1, y = 1*log(7) = .84509804<BR>\n" );
document.write( "when x = 3, y = 3*log(7) = 2.53529412<BR>\n" );
document.write( "when x = 5, y = 5*log(7) = 4.2254902<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you find the x value of each pair and then the y value of each pair and you place your point on the intersection of the x value and y value.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you do this for each coordinate pair in turn.<BR>\n" );
document.write( "a coordinate pair would be an x value with its corresponding y value.<BR>\n" );
document.write( "example:<BR>\n" );
document.write( "when x = 3, y = 2.53529412<BR>\n" );
document.write( "your coordinate pair is (3,2.53529412)<BR>\n" );
document.write( "when x = -3, y = -2.53529412<BR>\n" );
document.write( "your coordinate pair is (-3,-2.53529412)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your graph will look like this:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-8%2C%2B8%2C-5%2C5%2Cln%287%5Ex%29%2Fln%2810%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-8%2C%2B8%2C-5%2C5%2Cln%287%5Ex%29%2Fln%2810%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "This graph looks like a straight line.  <BR>\n" );
document.write( "logarithms do that.<BR>\n" );
document.write( "They take an exponential equation and make them look like straight lines when you take the log of them.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "A graph of 7^x would look like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C-20000%2C20000%2C7%5Ex%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C10%2C-20000%2C20000%2C7%5Ex%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The graph of log(7^x) looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-8%2C%2B8%2C-5%2C5%2Cln%287%5Ex%29%2Fln%2810%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-8%2C%2B8%2C-5%2C5%2Cln%287%5Ex%29%2Fln%2810%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "when x = 5, y = 7^x = 16807 while y = log(7^x) = 4.2254902<BR>\n" );
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document.write( "This has to do with the nature of logarithms.<BR>\n" );
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document.write( "The basic formula for logarithms is that the log(x) = y if and only if 10^y = x<BR>\n" );
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document.write( "An example:<BR>\n" );
document.write( "log(1000) = 3 if and only if 10^3 = 1000<BR>\n" );
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document.write( "In our formula, we have:<BR>\n" );
document.write( "log(7^5) = log(16807) = 4.2254902<BR>\n" );
document.write( "This means that 10^4.2254902 = 16807.<BR>\n" );
document.write( "You can use your calculator to prove this is true.<BR>\n" );
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document.write( "The equation of log(7^x) does not have an asymptote.<BR>\n" );
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document.write( "A fairly decent definition of asymptote can be found at the following web address:<BR>\n" );
document.write( "http://www.wordiq.com/definition/Asymptote<BR>\n" );
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document.write( "If you need extra help with understanding exponents and logarithms, or any other topics in algegbra, then you can go to the following website where help would be available.<BR>\n" );
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document.write( "http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/index.htm<BR>\n" );
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document.write( "The tutorials you would be interested in dealing with exponents would be:<BR>\n" );
document.write( "Tutorial 2,5,19,42,45,47<BR>\n" );
document.write( "The tutorials you would be interested in dealing with logarithms would be:<BR>\n" );
document.write( "43,44,46,47<BR>\n" );
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document.write( "If this website doesn't suit your fancy, you can find others by doing a search on \"algebra tutorials\" or \"algebra lessons\" or on anything you are having trouble with, like \"exponential equations\" or \"logarithms\" or \"logarithmic equations\".<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );