document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=235064>Question 235064</A>: <I><SPAN STYLE=\"word-break: break-all;\"> write each of the following as a single logarithm<BR>\n" );
document.write( " a. 3In2+In (x^2)+2<BR>\n" );
document.write( "answer 3In^2<BR>\n" );
document.write( " b.1/2 loga 4-2 loga 5<BR>\n" );
document.write( "answer loga4^1/2-log 5^2\r<BR>\n" );
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document.write( "can u please help me </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #173255 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=173255\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "a.<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 3\,\cdot\,\ln(2)\ +\ \ln(x^2)\ +\ 2\">\r<BR>\n" );
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document.write( "The first thing to do is look at the definition of a logarithm.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ \ b^y = x \Rightarrow\ \ y = \log_b(x)\">  \r<BR>\n" );
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document.write( "The base of the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ln\"> function is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large e\">, so we can say that:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ \ e^2 = x \Rightarrow\ \ 2 = \log_e(e^2)\">\r<BR>\n" );
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document.write( "So we can now re-write your problem:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 3\,\cdot\,\ln(2)\ +\ \ln(x^2)\ +\ \ln(e^2)\">\r<BR>\n" );
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document.write( "Now use:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \log_b(x^n) = n\log_b(x)\">\r<BR>\n" );
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document.write( "To say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ln(2^3)\ +\ \ln(x^2)\ +\ \ln(e^2)\">\r<BR>\n" );
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document.write( "and simplify to:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ln(8)\ +\ \ln(x^2)\ +\ \ln(e^2)\">\r<BR>\n" );
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document.write( "Now use the property that the sum of the logs is the log of the product, that is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \log_b(x) + \log_b(y) = \log_b(xy)\">\r<BR>\n" );
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document.write( "to write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 3\,\cdot\,\ln(2)\ +\ \ln(x^2)\ +\ 2\ =\ \ln(8e^2x^2)\ \approx \ln(59.11x^2)\">\r<BR>\n" );
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document.write( "==========================================================================\r<BR>\n" );
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document.write( "b.<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{2}\,\cdot\,\log_a(4)\ -\ 2\,\cdot\,\log_a(5)\">\r<BR>\n" );
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document.write( "Use\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \log_b(x^n) = n\log_b(x)\">\r<BR>\n" );
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document.write( "To say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \log_a(4^{\frac{1}{2}})\ -\ \log_a(5^2)\">\r<BR>\n" );
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document.write( "Recall that:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a^{\frac{1}{n}} = \sqrt[n]{a}\">\r<BR>\n" );
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document.write( "To say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \log_a(2)\ -\ \log_a(25)\">\r<BR>\n" );
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document.write( "Now use the property that the difference of the logs is the log of the quotient, that is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \log_b(x) - \log_b(y) = \log_b\left(\frac{x}{y}\right)\">\r<BR>\n" );
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document.write( "To say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{2}\,\cdot\,\log_a(4)\ -\ 2\,\cdot\,\log_a(5)\ =\ \log_a\left(\frac{2}{25}\right)\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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