document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=380915>Question 380915</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the expression log2(6x/y) as a sum and/ or difference of logarithms </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #270327 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=270327\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> log(2,6x/y) is equal to the log of 6x/y to the base of 2.\r<BR>\n" );
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document.write( "it means the same as what you wrote as log2(6x/y).\r<BR>\n" );
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document.write( "the notation, however, is more in line with the way the algebra.com formula generators work.\r<BR>\n" );
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document.write( "using the algebra.com formula generator, log(2,6x/y) will show up as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C6x%2Fy%29 ALIGN=MIDDLE  ALT=\"log%282%2C6x%2Fy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "All you do is put 3 { in front of it and 3 } behind it.\r<BR>\n" );
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document.write( "in general, log(x/y) = log(x) - log(y)\r<BR>\n" );
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document.write( "your equation becomes:\r<BR>\n" );
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document.write( "log(2,6x/y) = log(2,6x) - log(2,y)\r<BR>\n" );
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document.write( "in general, log (x*y) = log(x) + log(y)\r<BR>\n" );
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document.write( "your equation becomes:\r<BR>\n" );
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document.write( "log(2,6x/y) = log(2,6) + log(2,x) - log(y)\r<BR>\n" );
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document.write( "the concept is the same regardless of the base.\r<BR>\n" );
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document.write( "if the base were 10, then it would be shown as:\r<BR>\n" );
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document.write( "log(10,6x/y) = log(10,6) + log(10,x) - log(10,y)\r<BR>\n" );
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document.write( "to show you how it works, we'll use log to the base 10 because your calculator can handle that.\r<BR>\n" );
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document.write( "also, log(10,x) is normally shown as log(x).\r<BR>\n" );
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document.write( "the base of 10 is implied.\r<BR>\n" );
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document.write( "let's take log(6*15/30)\r<BR>\n" );
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document.write( "this should be translated to log(6) + log(15) - log(30) which is the same treatment we provided above.\r<BR>\n" );
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document.write( "using our calculator, we get log(6*15/30) = log(3) = .477121255\r<BR>\n" );
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document.write( "using our calculator again, we get log(6) + log(15) - log(30) = :\r<BR>\n" );
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document.write( ".77815125 + 1.176091259 - 1.477121255 = .477121255\r<BR>\n" );
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document.write( "we get the same answer, as we should.\r<BR>\n" );
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document.write( "same concepts works with any base, so the answer to your question is:\r<BR>\n" );
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document.write( "log(2,6x/y) = log(2,6) + log(2,x) - log(2,y).\r<BR>\n" );
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document.write( " </SPAN>\n" );
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