document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=890517>Question 890517</A>: <I><SPAN STYLE=\"word-break: break-all;\"> h(x) = ln(x + 9)<BR>\n" );
document.write( "To sketch the graph of the function, first rewrite the logarithmic equation in the exponential form.<BR>\n" );
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document.write( " ? = x + 9\r<BR>\n" );
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document.write( "Solve for x.<BR>\n" );
document.write( "x = ?<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 #539033 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=539033\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "the log equation is equivalent to the exponential equation as defined by the identity equation shown below:\r<BR>\n" );
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document.write( "logb(a) = y if and only if b^y = a\r<BR>\n" );
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document.write( "this statement reads:\r<BR>\n" );
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document.write( "log of a to the base of b is equal to y if and only if the base of b raised to the power of y is equal to a.\r<BR>\n" );
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document.write( "this works for any base, including the base of e which is what LN represents.\r<BR>\n" );
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document.write( "ln(x + 9) = loge(x + 9)\r<BR>\n" );
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document.write( "e is the scientific constant of 2.718281828...\r<BR>\n" );
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document.write( "this statement says that the natural log of (x + 9) is equal to the log of (x + 9) to the base of e.\r<BR>\n" );
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document.write( "your equation of ln(x + 9) is equivalent to loge(x + 9).\r<BR>\n" );
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document.write( "the log identity formula applied to your problem is:\r<BR>\n" );
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document.write( "loge(x+9) = y if and only if e^y = x + 9\r<BR>\n" );
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document.write( "if you solve for x in this equation, you get x = e^y - 9\r<BR>\n" );
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document.write( "instead of x being the independent variable, y is the independent variable.\r<BR>\n" );
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document.write( "the graph of y = ln(x+9) is identical to the graph of x = e^y - 9.\r<BR>\n" );
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document.write( "i'll show you  that further down.\r<BR>\n" );
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document.write( "normally you choose values for x and find the equivalent value of y through the use of the formula.\r<BR>\n" );
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document.write( "here you will choose values for y and find the equivalent value of x through the use of the formula.\r<BR>\n" );
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document.write( "then you graph the coordinate points that you have.\r<BR>\n" );
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document.write( "create a table with values for y from y = -4 to + 4 and calculate x = e^y - 9 for each value of y.\r<BR>\n" );
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document.write( "your table will look like this:\r<BR>\n" );
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document.write( "y     x\r\n" );
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document.write( "-4    -8.98\r\n" );
document.write( "-3    -8.95\r\n" );
document.write( "-2    -8.87\r\n" );
document.write( "-1    -8.63\r\n" );
document.write( " 0    -8.00\r\n" );
document.write( " 1    -6.28\r\n" );
document.write( " 2    -1.61\r\n" );
document.write( " 3     11.09\r\n" );
document.write( " 4     45.60\r\n" );
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document.write( "</PRE>\r<BR>\n" );
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document.write( "you are looking for the value of y and then finding the corresponding value of x.\r<BR>\n" );
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document.write( "the graph of your equation of x = e^y - 9 will look like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/080106.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "this is identical to the grah of y = ln(x+9) that is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/080107.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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