document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=212356>Question 212356</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am so confused with this problem.<BR>\n" );
document.write( "Express as a sum, difference, and product of logarithims, without using exponents.<BR>\n" );
document.write( "          3<BR>\n" );
document.write( "log b  &#8730; x^8/y^2z^5\r<BR>\n" );
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document.write( "I could not get it to show the way the problem does. It reads log (small b below) square root with 3 above the square root symbol. Inside the square root symbol it has x^8 over y^2z^5.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #160385 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=160385\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \log_{b}\left( \sqrt[3]{\frac{x^8}{y^2z^5}} \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_{b}\left( \left(\frac{x^8}{y^2z^5}\right)^{\frac{1}{3}} \right)\"> ... Convert to rational exponent notation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{3}\log_{b}\left( \frac{x^8}{y^2z^5} \right)\"> ... Pull down the exponent using the identity  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%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/rendertex.cgi?\LARGE \frac{1}{3}\left(\log_{b}\left(x^8\right)-\log_{b}\left(y^2z^5\right) \right)\"> ... Break up the log using the identity  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28A%2FB%29%29=log%28b%2C%28A%29%29-log%28b%2C%28B%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28A%2FB%29%29=log%28b%2C%28A%29%29-log%28b%2C%28B%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/rendertex.cgi?\LARGE \frac{1}{3}\left(\log_{b}\left(x^8\right)-\left(\log_{b}\left(y^2\right)+\log_{b}\left(z^5\right)\right) \right)\"> ... Break up the second log using the identity  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28A%2AB%29%29=log%28b%2C%28A%29%29%2Blog%28b%2C%28B%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28A%2AB%29%29=log%28b%2C%28A%29%29%2Blog%28b%2C%28B%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/rendertex.cgi?\LARGE \frac{1}{3}\left(\log_{b}\left(x^8\right)-\log_{b}\left(y^2\right)-\log_{b}\left(z^5\right) \right)\"> Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{3}\left(8\log_{b}\left(x\right)-2\log_{b}\left(y\right)-5\log_{b}\left(z\right) \right)\"> ... Pull down the exponents using the identity  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%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/rendertex.cgi?\LARGE \frac{8}{3}\log_{b}\left(x\right)-\frac{2}{3}\log_{b}\left(y\right)-\frac{5}{3}\log_{b}\left(z\right)\"> ... Distribute\r<BR>\n" );
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document.write( "So \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \log_{b}\left( \sqrt[3]{\frac{x^8}{y^2z^5}} \right) = \frac{8}{3}\log_{b}\left(x\right)-\frac{2}{3}\log_{b}\left(y\right)-\frac{5}{3}\log_{b}\left(z\right)\"> \r<BR>\n" );
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document.write( "assuming that every variable is positive. </SPAN>\n" );
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