document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167904>Question 167904</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help with this question \"Express as a single logarithm and, if possible, simplity.\"\r<BR>\n" );
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document.write( "1.  2/5 log(a)x - 1/3 log(a) y\r<BR>\n" );
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document.write( "2.  ln 2x + 3(1n x - ln y)\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 #123766 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=123766\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do the first one to get you started\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{2}{5}\log_{a}\left(x\right)-\frac{1}{3}\log_{a}\left(y\right)\"> Start with the given expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \log_{a}\left(x^{\frac{2}{5}}\right)-\log_{a}\left(y^{\frac{1}{3}}\right)\"> 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, take the coefficient that is in front of the logs and place them as exponents\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \log_{a}\left(\frac{x^{\frac{2}{5}}}{y^{\frac{1}{3}}}\right)\"> 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( "This next step is optional:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \log_{a}\left(\frac{\sqrt[5]{x^{2}}}{\sqrt[3]{y}}\right)\"> Convert from exponent notation to radical notation.\r<BR>\n" );
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document.write( "So the answer is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \log_{a}\left(\frac{x^{\frac{2}{5}}}{y^{\frac{1}{3}}}\right)\"> (which is in exponent notation) or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \log_{a}\left(\frac{\sqrt[5]{x^{2}}}{\sqrt[3]{y}}\right)\"> (which is in radical notation) </SPAN>\n" );
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