document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=270839>Question 270839</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is the original equation:\r<BR>\n" );
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document.write( "x=2^-(y-2)\r<BR>\n" );
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document.write( "What I have to apply to it is the following:   Transform the expression into the equivalent logarithmic equation; and 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. \r<BR>\n" );
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document.write( "I think the resulting equivalent logarithmic expression is:\r<BR>\n" );
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document.write( "log_2 (x) = -(y-2)\r<BR>\n" );
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document.write( "Am I correct?  And if I am, how to go about solving this to put it in graphing form?  Do I have to solve using the inverse?  Any help/advice is appreciated.  I really want to understand!  Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #198387 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=198387\">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=log%282%2C+%28x%29%29+=+-%28y-2%29 ALIGN=MIDDLE  ALT=\"log%282%2C+%28x%29%29+=+-%28y-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is correct so far. But there two more things to do. First of all, we should solve for y. So we'll multiply both sides by -1:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-log%282%2C+%28x%29%29+=+y-2 ALIGN=MIDDLE  ALT=\"-log%282%2C+%28x%29%29+=+y-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and then add 2 to each side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-log%282%2C+%28x%29%29+=+y ALIGN=MIDDLE  ALT=\"2-log%282%2C+%28x%29%29+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The second action is to change the base of the logarithm (unless you have a calculator that can find base 2 logarithms!?). Using the base conversion formala, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29 ALIGN=MIDDLE  ALT=\"log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to change the base 2 logarithm into a logarithm your calculator can calculate (base 10 or base e (ln) usually). I'll change to base 10:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-log%28%28x%29%29%2Flog%28%282%29%29+=+y ALIGN=MIDDLE  ALT=\"2-log%28%28x%29%29%2Flog%28%282%29%29+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since the instructions say to show your work and I believe the work should show you using the logarithmic equation, this is the equation that should be used for the rest of the problem.<br><BR>\n" );
document.write( "As for the evaluation of this equation with the various values of x, I'll leave that up to you. Just choose a value for x and use your calculator on the left side of the equation to find the y value for that x. Repeat this for all the various x values. This will give you at total of 7 pairs of coordinates to plot on the graph.<BR>\n" );
document.write( "Here's what your graph should look like when you are finished. (Note: The graph may look like it touches the y-axis. It does not. The y-axis is a vertical asymptote for this graph. Algebra.com's graphing feature is not perfect.)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C+400%2C+-2%2C+6%2C+-4%2C+4%2C+2-log%282%2C+x%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C+400%2C+-2%2C+6%2C+-4%2C+4%2C+2-log%282%2C+x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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