document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=212950>Question 212950</A>: <I><SPAN STYLE=\"word-break: break-all;\"> y = 2^x       x = 2^y\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 x =0.  Transform the second expression into the equivalent logarithmic equation;  and evaluate the logarithmic equation for three values of x that ar greater than 1, three values of x that are between 0 and 1, and at x = 1.  Use the resulting ordered pairs to plot the graph of each function.\r<BR>\n" );
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document.write( "On the first equation I got y = 2^x\r<BR>\n" );
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document.write( "X   Y   3 positives of x<BR>\n" );
document.write( "1   2<BR>\n" );
document.write( "2   4<BR>\n" );
document.write( "3   8\r<BR>\n" );
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document.write( "X   Y   3 negatives of x<BR>\n" );
document.write( "-1  -2<BR>\n" );
document.write( "-2  -4<BR>\n" );
document.write( "-3  -8\r<BR>\n" );
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document.write( "X    Y  x = 0<BR>\n" );
document.write( "0    2\r<BR>\n" );
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document.write( "I do not under stand the second part of this equation. Is the first part correct?\r<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 #160867 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=160867\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> No!  For y=2^x, when you use negative values for x, you do NOT get negative values for y! What you get is a fraction!\r<BR>\n" );
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document.write( "y=2^x<BR>\n" );
document.write( "If x=-1, then y=2^-1 = 1/2<BR>\n" );
document.write( "if x=-2, then y=2^-2 =1/4<BR>\n" );
document.write( "If x=-3, then y=2^-3=1/8\r<BR>\n" );
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document.write( "Then the second part of the equation seems strange to me. Let me take a look at it.  (You may find my explanation that I referenced below helpful for this part!)\r<BR>\n" );
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document.write( "Start with x=2^y, and change it to logarithmic form.  In this case, 2 is the base number, y is the exponent, and x is the result.  You can write this in logarithmic form as  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Cx%29=y ALIGN=MIDDLE  ALT=\"log%282%2Cx%29=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=log%282%2Cx%29 ALIGN=MIDDLE  ALT=\"y=log%282%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "Now, you are supposed to take 3 values of x that are greater than 1 (like x=2, 4, and 8, which would give you 3 values of y that are 1,2, and 3 respectively).  I don't know if how I got these numbers is clear to you, but that's what they want you to do!\r<BR>\n" );
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document.write( "Then take 3 values of x that are between 0 and 1 (like x=1/2, 1/4, and 1/8, which give you values of y that are -1, -2, and -3 respectively).  \r<BR>\n" );
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document.write( "If you graph these points, I suppose it should look like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C+-10%2C10%2C-10%2C10%2C+2%5Ex%2C+%28ln%28x%29%29%2F%28ln%282%29%29+%29+ ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C+-10%2C10%2C-10%2C10%2C+2%5Ex%2C+%28ln%28x%29%29%2F%28ln%282%29%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "See if that makes any sense to you!!  \r<BR>\n" );
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document.write( "You might want to look at my own explanation of LOGARITHMS in which I begin my explanation with the graphs of y=2^x compared to x=2^y.  I did a video a few years ago, and it is on my website for free if you want to see it.  Do a \"Bing\" search for my last name \"Rapalje\", and look for \"Rapalje Homepage.\"  Near the top of my Homepage, I have a link called \"Rapalje Videos\".  Click on that and choose \"College Algebra\".  Look for the two videos on Logarithms.  This would be the first one.  \r<BR>\n" );
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document.write( "I also have my written explanation of Logarithms.  From the top of my homepage, look for \"Basic, Intermediate, and College Algebra: One Step at a Time\", choose \"College Algebra\" and look for \"Chapter 4, Logarithms.\"  This is my own non-traditional explanation written for students who don't understand the traditional textbooks.\r<BR>\n" );
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document.write( "It might help you, and it's ALL free, like algebra.com! \r<BR>\n" );
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document.write( "R^2\r<BR>\n" );
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document.write( "Dr. Robert J. Rapalje, Retired<BR>\n" );
document.write( "Seminole Community College<BR>\n" );
document.write( "Altamonte Springs Campus<BR>\n" );
document.write( "Florida  </SPAN>\n" );
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