document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173557>Question 173557</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3^(x^2+20)=(1/27)^(3x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #128750 by </B><A HREF=/tutors/aboutme.mpl?userid=nycsub_teacher><B>nycsub_teacher(90)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nycsub_teacher><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=128750\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3^(x^2+20)=(1/27)^(3x)\r<BR>\n" );
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document.write( "The idea is to get the same base on both sides of the exponential equation.\r<BR>\n" );
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document.write( "We can express 1/27 as 3^(-3) because they both mean the same thing.\r<BR>\n" );
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document.write( "We now have this:\r<BR>\n" );
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document.write( "3^(x^2+20)= [3^(-3)]^(3x)\r<BR>\n" );
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document.write( "Do you see that we now have the same base 3 on both sides?\r<BR>\n" );
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document.write( "We now bring down the exponents and set them them equal to each other.\r<BR>\n" );
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document.write( "Before we do that, [3^(-3)]^(3x)becomes 3^(-9x).  Do you see how this happened?\r<BR>\n" );
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document.write( "3^(x^2 + 20) = 3^(-9x)\r<BR>\n" );
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document.write( "x^2 + 20 = -9x\r<BR>\n" );
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document.write( "x^2 + 9x + 20 = 0\r<BR>\n" );
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document.write( "We now have a quadratic equation that can be factored.\r<BR>\n" );
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document.write( "(x + 4) (x + 5) = 0\r<BR>\n" );
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document.write( "Set each factor equal to zero and solve for x.\r<BR>\n" );
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document.write( "x + 4 = 0\r<BR>\n" );
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document.write( "x = -4\r<BR>\n" );
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document.write( "=========\r<BR>\n" );
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document.write( "x + 5 = 0\r<BR>\n" );
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document.write( "x = -5\r<BR>\n" );
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document.write( "Did you follow?\r<BR>\n" );
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document.write( " </SPAN>\n" );
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