document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1153449>Question 1153449</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Express in a single logarithm,  ln x + a ln y − b ln z </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #775665 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=775665\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> two properties of logs are applicable here.\r<BR>\n" );
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document.write( "first is :\r<BR>\n" );
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document.write( "ln(x^a) = a * ln(x)\r<BR>\n" );
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document.write( "second is:\r<BR>\n" );
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document.write( "ln(x * y / z) = ln(x) * ln(y) - ln(z)\r<BR>\n" );
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document.write( "first gets you:\r<BR>\n" );
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document.write( "a * ln(y) = ln(y^a)\r<BR>\n" );
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document.write( "b * ln(z) = ln(z^b)\r<BR>\n" );
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document.write( "your formula starts with:\r<BR>\n" );
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document.write( "ln(x) + a * ln(y) - b * ln(z)\r<BR>\n" );
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document.write( "applying the first property above makes the expression above equivalent to:\r<BR>\n" );
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document.write( "ln(x) + ln(y^a) - ln(z^b)\r<BR>\n" );
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document.write( "second gets you:\r<BR>\n" );
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document.write( "ln(x * y^a / z^b) = ln(x) + ln(y^a) - ln(z^b)\r<BR>\n" );
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document.write( "here's a reference on properties of logarithms.\r<BR>\n" );
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document.write( "the log log function in your calculator is log(x) to the base of 10.\r<BR>\n" );
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document.write( "the ln function is log(x) in your calculator is log(x) to the base of e.\r<BR>\n" );
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document.write( "the properties of logs applies to both log function and ln function.\r<BR>\n" );
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document.write( "here's a couple of references on the properties of logs.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.montereyinstitute.org/courses/DevelopmentalMath/TEXTGROUP-1-19_RESOURCE/U18_L2_T2_text_final.html\" target = \"_blank\">http://www.montereyinstitute.org/courses/DevelopmentalMath/TEXTGROUP-1-19_RESOURCE/U18_L2_T2_text_final.html</a>\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.purplemath.com/modules/logrules.htm\" target = \"_blank\">https://www.purplemath.com/modules/logrules.htm</a> </SPAN>\n" );
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