document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=365680>Question 365680</A>: <I><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%28t%2F%28t-4%29%29=1+ ALIGN=MIDDLE  ALT=\"+ln%28t%2F%28t-4%29%29=1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solve for t. give exact answer. (no decimals)\r<BR>\n" );
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document.write( "thank you\r<BR>\n" );
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document.write( "   &#8710;<BR>\n" );
document.write( " &#8710; &#8710; </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #260661 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=260661\">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=+ln%28t%2F%28t-4%29%29=1+ ALIGN=MIDDLE  ALT=\"+ln%28t%2F%28t-4%29%29=1+\"   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=+ln%28t%2F%28t-4%29%29=ln%28e%29+ ALIGN=MIDDLE  ALT=\"+ln%28t%2F%28t-4%29%29=ln%28e%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite 1 as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28e%29 ALIGN=MIDDLE  ALT=\"ln%28e%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Recall that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28e%29=1 ALIGN=MIDDLE  ALT=\"ln%28e%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the logs have the same base (e), this means that the arguments (the stuff inside the logs) are equal.\r<BR>\n" );
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document.write( "Formally, if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28x%29=ln%28y%29 ALIGN=MIDDLE  ALT=\"ln%28x%29=ln%28y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y ALIGN=MIDDLE  ALT=\"x=y\"   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=+t%2F%28t-4%29=e+ ALIGN=MIDDLE  ALT=\"+t%2F%28t-4%29=e+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the property given above to set the arguments equal to each other.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t=e%28t-4%29+ ALIGN=MIDDLE  ALT=\"+t=e%28t-4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t-4 ALIGN=MIDDLE  ALT=\"t-4\"   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=+t=et-4e+ ALIGN=MIDDLE  ALT=\"+t=et-4e+\"   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=+t-et=-4e+ ALIGN=MIDDLE  ALT=\"+t-et=-4e+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract et from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%281-e%29=-4e+ ALIGN=MIDDLE  ALT=\"+t%281-e%29=-4e+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF 't'.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t=-4e%2F%281-e%29+ ALIGN=MIDDLE  ALT=\"+t=-4e%2F%281-e%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-e ALIGN=MIDDLE  ALT=\"1-e\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate 't'.\r<BR>\n" );
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document.write( "<font color=red>Optional Step:</font> You can rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-e ALIGN=MIDDLE  ALT=\"1-e\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-e%2B1=-%28e-1%29 ALIGN=MIDDLE  ALT=\"-e%2B1=-%28e-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and notice how the negatives cancel in the numerator and denominator. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=4e%2F%28e-1%29 ALIGN=MIDDLE  ALT=\"t=4e%2F%28e-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > also\r<BR>\n" );
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document.write( "So the solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t=-4e%2F%281-e%29+ ALIGN=MIDDLE  ALT=\"+t=-4e%2F%281-e%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You can also write the solution as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=4e%2F%28e-1%29 ALIGN=MIDDLE  ALT=\"t=4e%2F%28e-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the two are equivalent).\r<BR>\n" );
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document.write( "If you need more help, email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=Algebra%20Help\">jim_thompson5910@hotmail.com</a>\r<BR>\n" );
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document.write( "Also, feel free to check out my <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">tutoring website</a>\r<BR>\n" );
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document.write( "Jim </SPAN>\n" );
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