document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=88626>Question 88626</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve ln(5-x) = 12. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #64489 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=64489\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I agree with the solution by ankor (Carl).  Here's another way of looking at it:<BR>\n" );
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document.write( "Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%285-x%29+=+12 ALIGN=MIDDLE  ALT=\"ln%285-x%29+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This equation can be solved by converting the logarithmic form to the exponential <BR>\n" );
document.write( "form.  This conversion is defined by the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2CN%29=+y ALIGN=MIDDLE  ALT=\"log%28a%2CN%29=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "In which a is the base of the logarithm. By definition this logarithmic form is equivalent <BR>\n" );
document.write( "to the exponential form:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Ey+=+N ALIGN=MIDDLE  ALT=\"a%5Ey+=+N\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "By comparing the logarithmic form to the given problem you can see that N = (5 – x) and <BR>\n" );
document.write( "y = 12.  The value of  “a” is not quite as straightforward. Natural logarithms, designated by <BR>\n" );
document.write( "the use of “ln” is equivalent to log to the base “e” in which e = 2.718181828.  So <BR>\n" );
document.write( "“a” = “e” = 2.718281828. If you substitute these given values into the exponential form <BR>\n" );
document.write( "you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E12+=+5+%96+x ALIGN=MIDDLE  ALT=\"e%5E12+=+5+%96+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Since e = 2.718281828 this equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282.718281828%29%5E12+=+5+%96+x+ ALIGN=MIDDLE  ALT=\"%282.718281828%29%5E12+=+5+%96+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "A scientific calculator can be used to raise e to the 12th power. When you do that you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=162754.7914+=+5+%96+x ALIGN=MIDDLE  ALT=\"162754.7914+=+5+%96+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Adding x to both sides converts this equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+162754.7914+=+5+ ALIGN=MIDDLE  ALT=\"x+%2B+162754.7914+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Then subtracting 162754.7914 from both sides results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-162749.7914 ALIGN=MIDDLE  ALT=\"+x+=+-162749.7914\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Check this answer by returning to the original equation and substituting -162749.7914 <BR>\n" );
document.write( "for x.  This results in ln(5-(-162749.7914)) which becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%285+%2B162749.7914%29+=+12 ALIGN=MIDDLE  ALT=\"ln%285+%2B162749.7914%29+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28162754.7914%29+=+12 ALIGN=MIDDLE  ALT=\"ln%28162754.7914%29+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And using a scientific calculator you can enter 162754.7914 and press the ln key to find <BR>\n" );
document.write( "that ln(162754.7914) does in fact equal 12. So the answer for x is correct. It does <BR>\n" );
document.write( "equal -162749.7914.<BR>\n" );
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document.write( "Hope this helps you to see another way ... transferring from logarithmic form to exponential <BR>\n" );
document.write( "form is often a useful method in solving logarithmic equations.<BR>\n" );
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