document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=464432>Question 464432</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove that log 3=(log 2)+ (1/2)-(1/8)+(1/24)-(1/64)+....and so on. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #318158 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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/cgi-bin/show-face.mpl?user=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=318158\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is true if and only if\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{2} - \frac{1}{8} + \frac{1}{24} - \frac{1}{64} + ... = \ln {\frac{3}{2}}\">,\r<BR>\n" );
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document.write( "because it will satisfy the logarithm identity <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\log(ab) = \log(a) + \log(b)\">. However, the above series is equal to ln 3/2. If you know the Taylor series for ln x centered at 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ln{x} = (x-1) - \frac{1}{2}(x-1)^2 + \frac{1}{3}(x-1)^3...\">\r<BR>\n" );
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document.write( "We can replace x = 3/2 and get a true result. Hence the original equation is true. </SPAN>\n" );
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