document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=316702>Question 316702</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please show me how to do the following problem: Find all real solutions to the equations a) ln^2x-5ln^x=-6<BR>\n" );
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document.write( "                 b) 2 * ln(x)= ln(36)<BR>\n" );
document.write( "thank you!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #226657 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=226657\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We're going to use the following identities/properties:\r<BR>\n" );
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document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Aln%28x%29=ln%28x%5Ey%29 ALIGN=MIDDLE  ALT=\"y%2Aln%28x%29=ln%28x%5Ey%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28A%29-ln%28B%29=ln%28A%2FB%29 ALIGN=MIDDLE  ALT=\"ln%28A%29-ln%28B%29=ln%28A%2FB%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "3) If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28x%29=ln%28y%29 ALIGN=MIDDLE  ALT=\"ln%28x%29=ln%28y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y ALIGN=MIDDLE  ALT=\"x=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a) \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%282x%29-5%2Aln%28x%29=-6 ALIGN=MIDDLE  ALT=\"ln%282x%29-5%2Aln%28x%29=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%282x%29-ln%28x%5E5%29=-6 ALIGN=MIDDLE  ALT=\"ln%282x%29-ln%28x%5E5%29=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use identity #1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28%282x%29%2F%28x%5E5%29%29=-6 ALIGN=MIDDLE  ALT=\"ln%28%282x%29%2F%28x%5E5%29%29=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use identity #2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%29%2F%28x%5E5%29=e%5E%28-6%29 ALIGN=MIDDLE  ALT=\"%282x%29%2F%28x%5E5%29=e%5E%28-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Convert the equation into exponential form.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%29%2F%28x%5E5%29=1%2Fe%5E6 ALIGN=MIDDLE  ALT=\"%282x%29%2F%28x%5E5%29=1%2Fe%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-6%29 ALIGN=MIDDLE  ALT=\"e%5E%28-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fe%5E6 ALIGN=MIDDLE  ALT=\"1%2Fe%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%28x%5E4%29=1%2Fe%5E6 ALIGN=MIDDLE  ALT=\"2%2F%28x%5E4%29=1%2Fe%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce the expression on the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=%281%2Fe%5E6%29x%5E4 ALIGN=MIDDLE  ALT=\"2=%281%2Fe%5E6%29x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4 ALIGN=MIDDLE  ALT=\"x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2e%5E6=x%5E4 ALIGN=MIDDLE  ALT=\"2e%5E6=x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E6 ALIGN=MIDDLE  ALT=\"e%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4=2e%5E6 ALIGN=MIDDLE  ALT=\"x%5E4=2e%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Flip the equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=root%284%2C2e%5E6%29 ALIGN=MIDDLE  ALT=\"x=root%284%2C2e%5E6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the fourth root of both sides.\r<BR>\n" );
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document.write( "So the solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=root%284%2C2e%5E6%29 ALIGN=MIDDLE  ALT=\"x=root%284%2C2e%5E6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Aln%28x%29=ln%2836%29 ALIGN=MIDDLE  ALT=\"2%2Aln%28x%29=ln%2836%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28x%5E2%29=ln%2836%29 ALIGN=MIDDLE  ALT=\"ln%28x%5E2%29=ln%2836%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use identity #1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=36 ALIGN=MIDDLE  ALT=\"x%5E2=36\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use property #3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%2836%29 ALIGN=MIDDLE  ALT=\"x=sqrt%2836%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides (note: we're ignoring the negative square root since you can't take the log of a negative number).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6 ALIGN=MIDDLE  ALT=\"x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of 36 to get 6.\r<BR>\n" );
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document.write( "So the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6 ALIGN=MIDDLE  ALT=\"x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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