document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=922516>Question 922516</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need step-by-step to solve this equation:\r<BR>\n" );
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document.write( "4^(1-x)=3^(2x-5) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #559599 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20059)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=559599\">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=4%5E%281-x%29=3%5E%282x-5%29 ALIGN=MIDDLE  ALT=\"4%5E%281-x%29=3%5E%282x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We take the log of both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%5E%281-x%29%29=log%283%5E%282x-5%29%29 ALIGN=MIDDLE  ALT=\"log%284%5E%281-x%29%29=log%283%5E%282x-5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "There is a rule of logarithms that allows us to move an exponent<BR>\n" );
document.write( "in front as a multiplier of the log:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-x%29log%284%29=%282x-5%29log%283%29 ALIGN=MIDDLE  ALT=\"%281-x%29log%284%29=%282x-5%29log%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To make things easier let log(4)=A and log(3)=B\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-x%29A=%282x-5%29B ALIGN=MIDDLE  ALT=\"%281-x%29A=%282x-5%29B\"   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=A%281-x%29=B%282x-5%29 ALIGN=MIDDLE  ALT=\"A%281-x%29=B%282x-5%29\"   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=A-Ax=2Bx-5B ALIGN=MIDDLE  ALT=\"A-Ax=2Bx-5B\"   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=A%2B5B=2Bx%2BAx ALIGN=MIDDLE  ALT=\"A%2B5B=2Bx%2BAx\"   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=A%2B5B=%282B%2BA%29x ALIGN=MIDDLE  ALT=\"A%2B5B=%282B%2BA%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide both sides of the equation by (2B+A)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28A%2B5B%29%2F%282B%2BA%29=x ALIGN=MIDDLE  ALT=\"%28A%2B5B%29%2F%282B%2BA%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now replace A and B by the logs they represent:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28log%284%29%2B5%2Alog%283%29%29%2F%282%2Alog%283%29%2Blog4%29=x ALIGN=MIDDLE  ALT=\"%28log%284%29%2B5%2Alog%283%29%29%2F%282%2Alog%283%29%2Blog4%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "With a calculator we get\r<BR>\n" );
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document.write( "1.919720789 = x\r<BR>\n" );
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document.write( "Edwin</pre> </SPAN>\n" );
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