document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=242511>Question 242511</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the expression as the sum or difference of single logarithms x and y\r<BR>\n" );
document.write( "\n" );
document.write( "log^7 (2x/7) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #177554 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=177554\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I sincerely hope you meant:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \log_7\left(\frac{2x}{7}\right)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "rather than:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \log_{10}^7\left(\frac{2x}{7}\right)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "which is what you actually wrote.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Going with my initial assumption:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The difference of the logs is the log of the quotient:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \log_7\left(\frac{2x}{7}\right)\ =\ \log_7\left(2x\right)\ -\ \log_7\left(7\right)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The sum of the logs is the log of the product:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \log_7\left(2x\right)\ -\ \log_7\left(7\right)\ =\ \log_7\left(x\right)\ +\ \log_7\left(2\right)\ -\ \log_7\left(7\right)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The log to the base b of b is 1:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \log_7\left(x\right)\ +\ \log_7\left(2\right)\ -\ \log_7\left(7\right)\ =\ \log_7\left(x\right)\ +\ \log_7\left(2\right)\ -\ 1\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );