document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189948>Question 189948</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve each equation for x.\r<BR>\n" );
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document.write( "4+10^3-x=106\r<BR>\n" );
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document.write( "ln(x^2+x)=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142518 by </B><A HREF=/tutors/aboutme.mpl?userid=cutepiscean5><B>cutepiscean5(19)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=cutepiscean5><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=142518\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Lets take the first equation:\r<BR>\n" );
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document.write( "4+10^3-x=106\r<BR>\n" );
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document.write( "I shall consider the given equation written as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4+%2B+10%5E%283-x%29+=+106+ ALIGN=MIDDLE  ALT=\"+4+%2B+10%5E%283-x%29+=+106+\"   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=+10%5E%283-x%29+=+106+-+4 ALIGN=MIDDLE  ALT=\"+10%5E%283-x%29+=+106+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10%5E%283-x%29+=+102+ ALIGN=MIDDLE  ALT=\"+10%5E%283-x%29+=+102+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Taking log on both sides of the equation we get:\r<BR>\n" );
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document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log+10%5E%283-x%29+=+log+%28102%29+ ALIGN=MIDDLE  ALT=\"+log+10%5E%283-x%29+=+log+%28102%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "using the log properties that: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28a%5Em%29+=+mlog%28a%29+ ALIGN=MIDDLE  ALT=\"+log%28a%5Em%29+=+mlog%28a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get:\r<BR>\n" );
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document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%283-x%29log%2810%29+=+log%28102%29+ ALIGN=MIDDLE  ALT=\"+%283-x%29log%2810%29+=+log%28102%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "using log(10) = 1 and log(102) = 2.0086, we get:\r<BR>\n" );
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document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3-x+=+2.0086+ ALIGN=MIDDLE  ALT=\"+3-x+=+2.0086+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+3+-+2.0086+ ALIGN=MIDDLE  ALT=\"+x+=+3+-+2.0086+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+0.9913+ ALIGN=MIDDLE  ALT=\"+x+=+0.9913+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solving the second equation we get:\r<BR>\n" );
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document.write( "ln(x^2+x)=1\r<BR>\n" );
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document.write( "using the log property that if, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%28a%29+=+x+ ALIGN=MIDDLE  ALT=\"+ln%28a%29+=+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > , then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+e%5Ex+ ALIGN=MIDDLE  ALT=\"+a+=+e%5Ex+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+%2B+x+=+e%5E1+ ALIGN=MIDDLE  ALT=\"+x%5E2+%2B+x+=+e%5E1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+%2B+x+-+e+=+0+ ALIGN=MIDDLE  ALT=\"+x%5E2+%2B+x+-+e+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solving using the quadratic formula we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "here , a = 1, b = 1 and c = -e\r<BR>\n" );
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document.write( "thus,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-e%29+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-e%29+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-1+%2B+sqrt%28+1+%2B+4%2Ae%29%29%2F2+ ALIGN=MIDDLE  ALT=\"+x+=+%28-1+%2B+sqrt%28+1+%2B+4%2Ae%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-1+-+sqrt%28+1+%2B+4%2Ae%29%29%2F2+ ALIGN=MIDDLE  ALT=\"+x+=+%28-1+-+sqrt%28+1+%2B+4%2Ae%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you can further simplify this by plugging in the value of e as 2.718, and solving. It depends on how the answer is required.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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