document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189078>Question 1189078</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Express as a sum or difference of logarithms:\r<BR>\n" );
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document.write( "1) log a x^y/z^4<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 #820300 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=820300\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the expression is:\r<BR>\n" );
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document.write( "loga(x^y/z^4)<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "loga(x^y) - loga(z^4) which becomes:<BR>\n" );
document.write( "yloga(x) - 4loga(z)\r<BR>\n" );
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document.write( "to confirm this is true, let:<BR>\n" );
document.write( "a = 10<BR>\n" );
document.write( "y = 5<BR>\n" );
document.write( "z = 3<BR>\n" );
document.write( "x = 2\r<BR>\n" );
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document.write( "loga(x^y/z^4) becomes log(2^5)/3^4) = -.4033350406\r<BR>\n" );
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document.write( "yloga(x) - 4loga(z) becomes 5log(2) - 4log3) = -.403335046.\r<BR>\n" );
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document.write( "they're the same, confirming the transformation is correct.\r<BR>\n" );
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document.write( "not that loga = log10 = log function of your calculator.\r<BR>\n" );
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document.write( "also:\r<BR>\n" );
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document.write( "log(a/b) = log(a) - log(b)\r<BR>\n" );
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document.write( "also:\r<BR>\n" );
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document.write( "log(x^a) = alog(x)\r<BR>\n" );
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document.write( "here's a reference on log function that might help you to understand.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.chilimath.com/lessons/advanced-algebra/logarithm-rules/\" target = \"_blank\">https://www.chilimath.com/lessons/advanced-algebra/logarithm-rules/</a>\r<BR>\n" );
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document.write( "let me know if you have any questions.\r<BR>\n" );
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document.write( "theo\r<BR>\n" );
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