document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202903>Question 202903</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3000e%5E%280.17x%29+=+4000 ALIGN=MIDDLE  ALT=\"3000e%5E%280.17x%29+=+4000\"   DISABLED_style= \"max-width:90%; height:auto;\" > for x to four decimal places. The number e is the base of the natural logarithm function.\r<BR>\n" );
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document.write( "thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153067 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=153067\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Whenever you are asked to \"Solve for x\" it means: \"Use Algebra to change the equation around so that \"x\" is isolated (by itself) on one side of the equation\".<br><BR>\n" );
document.write( "In your equation we need to use Algebra to \"peel away\" the 3000, the \"e\" and the 0.17 and we need x out of the exponent. We can deal the the 3000 easily. Just divide both sides of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3000e%5E%280.17x%29+=+4000 ALIGN=MIDDLE  ALT=\"3000e%5E%280.17x%29+=+4000\"   DISABLED_style= \"max-width:90%; height:auto;\" > by 3000 giving:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283000e%5E%280.17x%29%29%2F3000+=+4000%2F3000 ALIGN=MIDDLE  ALT=\"%283000e%5E%280.17x%29%29%2F3000+=+4000%2F3000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%280.17x%29+=+4%2F3 ALIGN=MIDDLE  ALT=\"e%5E%280.17x%29+=+4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In general when one has an equation of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Ex+=+b ALIGN=MIDDLE  ALT=\"a%5Ex+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" > you use the base \"a\" logarithm to eliminate the \"a\" <b>and</b> to get the \"x\" out of the exponent at the same time. So we can deal with both the \"e\" and the fact that x is in an exponent by finding the ln (the base \"e\" logarithm) of both sides.:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28e%5E%280.17x%29%29+=+ln%284%2F3%29 ALIGN=MIDDLE  ALT=\"ln%28e%5E%280.17x%29%29+=+ln%284%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28a%5Eb%29+=+b%2Aln%28a%29 ALIGN=MIDDLE  ALT=\"ln%28a%5Eb%29+=+b%2Aln%28a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > property on the left side we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.17x%29%2Aln%28e%29+=+ln%284%2F3%29 ALIGN=MIDDLE  ALT=\"%280.17x%29%2Aln%28e%29+=+ln%284%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since the ln(e) = 1 we now have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.17x+=+ln%284%2F3%29 ALIGN=MIDDLE  ALT=\"0.17x+=+ln%284%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now \"x\" is out of the exponent and \"e\" is gone! The final step is to divide both sides by 0.17:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.17x%29%2F%280.17%29+=+%28ln%284%2F3%29%29%2F%280.17%29 ALIGN=MIDDLE  ALT=\"%280.17x%29%2F%280.17%29+=+%28ln%284%2F3%29%29%2F%280.17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The 0.17's on the left side cancel giving:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28ln%284%2F3%29%29%2F%280.17%29 ALIGN=MIDDLE  ALT=\"x+=+%28ln%284%2F3%29%29%2F%280.17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We have \"solved for x\"! It is by itself on the left side of this equation. The only thing left to do is to simplify the right side. Using our calculators to find the ln(4/3) we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%280.2876820724517809%29%2F%280.17%29 ALIGN=MIDDLE  ALT=\"x+=+%280.2876820724517809%29%2F%280.17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and then dividing by 0.17:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1.6922474850104760 ALIGN=MIDDLE  ALT=\"x+=+1.6922474850104760\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And rounding to 4 decimal places:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1.6922 ALIGN=MIDDLE  ALT=\"x+=+1.6922\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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