document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=149398>Question 149398</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the exponential or logarithmic equations. (Write your final answer in BOTH exact and approximate value).\r<BR>\n" );
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document.write( "(a) 6^x-3 = 2^x\r<BR>\n" );
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document.write( "(b) log(5x-6) = 2log x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #109613 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=109613\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do the first one to get you started.\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=6%5E%28x-3%29+=+2%5Ex ALIGN=MIDDLE  ALT=\"6%5E%28x-3%29+=+2%5Ex\"   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=log%2810%2C%286%5E%28x-3%29%29%29+=+log%2810%2C%282%5Ex%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%286%5E%28x-3%29%29%29+=+log%2810%2C%282%5Ex%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > 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=%28x-3%29log%2810%2C%286%29%29+=+x%2Alog%2810%2C%282%29%29 ALIGN=MIDDLE  ALT=\"%28x-3%29log%2810%2C%286%29%29+=+x%2Alog%2810%2C%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite  both sides using the identity  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%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%2Alog%2810%2C%286%29%29-3log%2810%2C%286%29%29+=+x%2Alog%2810%2C%282%29%29 ALIGN=MIDDLE  ALT=\"x%2Alog%2810%2C%286%29%29-3log%2810%2C%286%29%29+=+x%2Alog%2810%2C%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Alog%2810%2C%286%29%29-3log%2810%2C%286%29%29-x%2Alog%2810%2C%282%29%29=0 ALIGN=MIDDLE  ALT=\"x%2Alog%2810%2C%286%29%29-3log%2810%2C%286%29%29-x%2Alog%2810%2C%282%29%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Alog%2810%2C%282%29%29 ALIGN=MIDDLE  ALT=\"x%2Alog%2810%2C%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Alog%2810%2C%286%29%29-x%2Alog%2810%2C%282%29%29=3log%2810%2C%286%29%29 ALIGN=MIDDLE  ALT=\"x%2Alog%2810%2C%286%29%29-x%2Alog%2810%2C%282%29%29=3log%2810%2C%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3log%2810%2C%286%29%29 ALIGN=MIDDLE  ALT=\"3log%2810%2C%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28log%2810%2C%286%29%29-log%2810%2C%282%29%29%29=3log%2810%2C%286%29%29 ALIGN=MIDDLE  ALT=\"x%28log%2810%2C%286%29%29-log%2810%2C%282%29%29%29=3log%2810%2C%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF \"x\"\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28log%2810%2C%286%2F2%29%29%29=3log%2810%2C%286%29%29 ALIGN=MIDDLE  ALT=\"x%28log%2810%2C%286%2F2%29%29%29=3log%2810%2C%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the logs using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28A%29%29-log%28b%2C%28B%29%29=log%28b%2C%28A%2FB%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28A%29%29-log%28b%2C%28B%29%29=log%28b%2C%28A%2FB%29%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%28log%2810%2C%283%29%29%29=3log%2810%2C%286%29%29 ALIGN=MIDDLE  ALT=\"x%28log%2810%2C%283%29%29%29=3log%2810%2C%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3log%2810%2C%286%29%29%2F%28log%2810%2C%283%29%29%29 ALIGN=MIDDLE  ALT=\"x=3log%2810%2C%286%29%29%2F%28log%2810%2C%283%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%283%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=log%2810%2C%286%5E3%29%29%2F%28log%2810%2C%283%29%29%29 ALIGN=MIDDLE  ALT=\"x=log%2810%2C%286%5E3%29%29%2F%28log%2810%2C%283%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the expression using the identity  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Alog%28b%2C%28x%29%29=log%28b%2C%28x%5Ey%29%29 ALIGN=MIDDLE  ALT=\"y%2Alog%28b%2C%28x%29%29=log%28b%2C%28x%5Ey%29%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=log%2810%2C%28216%29%29%2F%28log%2810%2C%283%29%29%29 ALIGN=MIDDLE  ALT=\"x=log%2810%2C%28216%29%29%2F%28log%2810%2C%283%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Raise 6 to the 3rd power to get 216\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=log%283%2C%28216%29%29 ALIGN=MIDDLE  ALT=\"x=log%283%2C%28216%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the change of base formula to rewrite the right side.\r<BR>\n" );
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document.write( "So the exact answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=log%283%2C%28216%29%29 ALIGN=MIDDLE  ALT=\"x=log%283%2C%28216%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which approximates to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4.892789 ALIGN=MIDDLE  ALT=\"x=4.892789\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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