document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=744709>Question 744709</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. Solve the following exponential equations<BR>\n" );
document.write( "a) 3^(2x-1) = 2^(x+2)<BR>\n" );
document.write( "b) 2^(x+1) = 5^(1-x)<BR>\n" );
document.write( "c) 2^(x+1)/ 5^x = 3\r<BR>\n" );
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document.write( "Can you please help me out? Thanks so much in advance:)<BR>\n" );
document.write( "Can you please show all the steps it would really help me understand:)\r<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 #453520 by </B><A HREF=/tutors/aboutme.mpl?userid=tommyt3rd><B>tommyt3rd(5050)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=tommyt3rd><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=tommyt3rd><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=453520\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E%282x-1%29+=+2%5E%28x%2B2%29 ALIGN=MIDDLE  ALT=\"3%5E%282x-1%29+=+2%5E%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Expanding exponents...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E%282x%29%2A3%5E%28-1%29+=+2%5Ex%2A2%5E2 ALIGN=MIDDLE  ALT=\"3%5E%282x%29%2A3%5E%28-1%29+=+2%5Ex%2A2%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "simplifying...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E%282x%29%2F3+=+2%5Ex%2A4 ALIGN=MIDDLE  ALT=\"3%5E%282x%29%2F3+=+2%5Ex%2A4\"   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=%283%5E2%29%5Ex%2F3=4%2A2%5Ex ALIGN=MIDDLE  ALT=\"%283%5E2%29%5Ex%2F3=4%2A2%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Next we isolate x...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%5Ex%2F3=4%2A2%5Ex ALIGN=MIDDLE  ALT=\"9%5Ex%2F3=4%2A2%5Ex\"   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=9%5Ex%2F2%5Ex=4%2A3 ALIGN=MIDDLE  ALT=\"9%5Ex%2F2%5Ex=4%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Key step: we can combine the bases under the exponent since the exponent for both of them is the same...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2F2%29%5Ex=12 ALIGN=MIDDLE  ALT=\"%289%2F2%29%5Ex=12\"   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=log%28%289%2F2%29%5Ex%29=log12 ALIGN=MIDDLE  ALT=\"log%28%289%2F2%29%5Ex%29=log12\"   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%2Alog%289%2F2%29=log12%29 ALIGN=MIDDLE  ALT=\"x%2Alog%289%2F2%29=log12%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=x=log12%2Flog%289%2F2%29 ALIGN=MIDDLE  ALT=\"x=log12%2Flog%289%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which can be rewritten as...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log12%2F%28log9-log2%29 ALIGN=MIDDLE  ALT=\"log12%2F%28log9-log2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Less steps for the remaining parts...\r<BR>\n" );
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document.write( "b)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%5E%28x%2B1%29+=+5%5E%281-x%29 ALIGN=MIDDLE  ALT=\"+2%5E%28x%2B1%29+=+5%5E%281-x%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=+2%5Ex%2A2+=+5%2A5%5E%28-x%29 ALIGN=MIDDLE  ALT=\"+2%5Ex%2A2+=+5%2A5%5E%28-x%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=2%5Ex%2F5%5Ex=5%2F2 ALIGN=MIDDLE  ALT=\"2%5Ex%2F5%5Ex=5%2F2\"   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=%282%2F5%29%5Ex=5%2F2 ALIGN=MIDDLE  ALT=\"%282%2F5%29%5Ex=5%2F2\"   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=%282%2F5%29%5Ex=5%2F2 ALIGN=MIDDLE  ALT=\"%282%2F5%29%5Ex=5%2F2\"   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=%282%2F5%29%5Ex=%282%2F5%29%5E%28-1%29 ALIGN=MIDDLE  ALT=\"%282%2F5%29%5Ex=%282%2F5%29%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "after taking log of both sides and cancelling (i.e. if the bases are equal the the exponents are also equal to each other)\r<BR>\n" );
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document.write( "x=-1\r<BR>\n" );
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document.write( "Now with maximum efficiency we solve the last...\r<BR>\n" );
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document.write( "c)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%28x%2B1%29%2F+5%5Ex+=+3 ALIGN=MIDDLE  ALT=\"2%5E%28x%2B1%29%2F+5%5Ex+=+3\"   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=%282%2A2%5Ex%29%2F5%5Ex=3 ALIGN=MIDDLE  ALT=\"%282%2A2%5Ex%29%2F5%5Ex=3\"   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=%282%2F5%29%5Ex=3%2F2 ALIGN=MIDDLE  ALT=\"%282%2F5%29%5Ex=3%2F2\"   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=log%28%282%2F5%29%5Ex%29=log%283%2F2%29 ALIGN=MIDDLE  ALT=\"log%28%282%2F5%29%5Ex%29=log%283%2F2%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=x=%28log3-log2%29%2F%28log2-log5%29 ALIGN=MIDDLE  ALT=\"x=%28log3-log2%29%2F%28log2-log5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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