document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205560>Question 1205560</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the point(s) of intersection of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%283%5Ex%29 ALIGN=MIDDLE  ALT=\"y=2%283%5Ex%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=6%282%5Ex%29 ALIGN=MIDDLE  ALT=\"y=6%282%5Ex%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > algebraically.  Round your answer to one decimal place. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842443 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=842443\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have two equations that you want to solve simultaneously (the same value of x applies to both equations).\r<BR>\n" );
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document.write( "the equations are:<BR>\n" );
document.write( "y = 2*3^x and y = 6*2^x.\r<BR>\n" );
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document.write( "set them equal to each other to get:<BR>\n" );
document.write( "2*3^x = 6*2^x\r<BR>\n" );
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document.write( "divide both sides of the equation by 2 to get:<BR>\n" );
document.write( "3^x = 3*2^x\r<BR>\n" );
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document.write( "divide both sides of the equation by 2^X to get:<BR>\n" );
document.write( "3^x / 2^x = 3\r<BR>\n" );
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document.write( "take the log of both dies of the equqtion to get:\r<BR>\n" );
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document.write( "log(3^x / 2^x) = log(3)\r<BR>\n" );
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document.write( "since log(a/b) = log(a) - log(b), you get:\r<BR>\n" );
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document.write( "log(3^x) - log(2^x) = log(3)\r<BR>\n" );
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document.write( "since log(a^b) = b*log(a), you get:\r<BR>\n" );
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document.write( "x * log(3) - x * log(2) = log(3)\r<BR>\n" );
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document.write( "factor out the x to get:\r<BR>\n" );
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document.write( "x * (log(3) - log(2) = log(3)\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = log(3) / (log(3) - log(2)) = 2.709511291.\r<BR>\n" );
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document.write( "the graph of both equations will intersect when the value of x is 2.709511291.\r<BR>\n" );
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document.write( "the value of y at that point will be 39.24600209.\r<BR>\n" );
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document.write( "here's the graph.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/010801.jpg\">\r<BR>\n" );
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document.write( "here's a reference on the properties of logs (also known as log rules).\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.chilimath.com/lessons/advanced-algebra/logarithm-rules/\" target = \"_blank\">https://www.chilimath.com/lessons/advanced-algebra/logarithm-rules/</a> </SPAN>\n" );
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