document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=86948>Question 86948</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve for the approximate value of x: In x=3<BR>\n" );
document.write( "Is it 3? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #62898 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=62898\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> By \"In\" I believe you mean \"ln\" which is the notation for natural logarithms. Natural<BR>\n" );
document.write( "logarithms have the base e which is the symbol for a number that is approximately 2.718281828 ...<BR>\n" );
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document.write( "This is a problem in which you can use a translation from logarithmic form to the equivalent<BR>\n" );
document.write( "exponential form. This translation is done according to the following rule:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Log%5Bb%5DA+=+C ALIGN=MIDDLE  ALT=\"Log%5Bb%5DA+=+C\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to the exponential form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5EC+=+A ALIGN=MIDDLE  ALT=\"b%5EC+=+A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "In your problem, the \"ln\" tells you that you are using a logarithm with the base e. Therefore,<BR>\n" );
document.write( "your problem can be written:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Log%5Be%5Dx=3 ALIGN=MIDDLE  ALT=\"Log%5Be%5Dx=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and by comparing this to the translation rule you can tell that b = e, C = 3, and A = x.<BR>\n" );
document.write( "Substitute these values into the exponential form and you get an exponential form of:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E3+=+x ALIGN=MIDDLE  ALT=\"e%5E3+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So you now know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+e%5E3 ALIGN=MIDDLE  ALT=\"x+=+e%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and since e is approximately 2.718281828 you can get<BR>\n" );
document.write( "an approximate value for x by using the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282.718281828%29%5E3 ALIGN=MIDDLE  ALT=\"x+=+%282.718281828%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can then use a calculator to cube 2.718281828 and you will get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=20.08553692 ALIGN=MIDDLE  ALT=\"x=20.08553692\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "as a pretty close approximation of the value of x.<BR>\n" );
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document.write( "Remember that translation form.  It's a fundamental definition for logarithms and it<BR>\n" );
document.write( "comes in quite handy for solving lots of logarithmic problems.<BR>\n" );
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