document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=169152>Question 169152</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Express as a single logarithm:\r<BR>\n" );
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document.write( "5logex+logey-2logez\r<BR>\n" );
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document.write( "All the e\"s are subscript.\r<BR>\n" );
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document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #124736 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=124736\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Alog%28e%2C%28x%29%29%2Blog%28e%2C%28y%29%29-2%2Alog%28e%2C%28z%29%29 ALIGN=MIDDLE  ALT=\"5%2Alog%28e%2C%28x%29%29%2Blog%28e%2C%28y%29%29-2%2Alog%28e%2C%28z%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28e%2C%28x%5E5%29%29%2Blog%28e%2C%28y%29%29-log%28e%2C%28z%5E2%29%29 ALIGN=MIDDLE  ALT=\"log%28e%2C%28x%5E5%29%29%2Blog%28e%2C%28y%29%29-log%28e%2C%28z%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the expression using the identity  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Alog%28b%2C%28x%29%29=log%28b%2C%28x%5Ey%29%29 ALIGN=MIDDLE  ALT=\"y%2Alog%28b%2C%28x%29%29=log%28b%2C%28x%5Ey%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, place the coefficients as exponents.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28e%2C%28x%5E5y%29%29-log%28e%2C%28z%5E2%29%29 ALIGN=MIDDLE  ALT=\"log%28e%2C%28x%5E5y%29%29-log%28e%2C%28z%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the first two logs using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28A%29%29%2Blog%28b%2C%28B%29%29=log%28b%2C%28A%2AB%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28A%29%29%2Blog%28b%2C%28B%29%29=log%28b%2C%28A%2AB%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28e%2C%28%28x%5E5y%29%2F%28z%5E2%29%29%29 ALIGN=MIDDLE  ALT=\"log%28e%2C%28%28x%5E5y%29%2F%28z%5E2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the logs using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28A%29%29-log%28b%2C%28B%29%29=log%28b%2C%28A%2FB%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28A%29%29-log%28b%2C%28B%29%29=log%28b%2C%28A%2FB%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Alog%28e%2C%28x%29%29%2Blog%28e%2C%28y%29%29-2%2Alog%28e%2C%28z%29%29 ALIGN=MIDDLE  ALT=\"5%2Alog%28e%2C%28x%29%29%2Blog%28e%2C%28y%29%29-2%2Alog%28e%2C%28z%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28e%2C%28%28x%5E5y%29%2F%28z%5E2%29%29%29 ALIGN=MIDDLE  ALT=\"log%28e%2C%28%28x%5E5y%29%2F%28z%5E2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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