document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=380916>Question 380916</A>: <I><SPAN STYLE=\"word-break: break-all;\"> write the expression (log base of b)(2y+5)-4(log base of b)(y+3) as a single<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 #270329 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=270329\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> that expression would be shown as:\r<BR>\n" );
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document.write( "log(b,(2y+5)) - 4*log(b,(y+3))\r<BR>\n" );
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document.write( "in general x * log(y) = log(y^x)\r<BR>\n" );
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document.write( "your expression becomes:\r<BR>\n" );
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document.write( "log(b,(2y+5)) - log(b,((y+3)^4))\r<BR>\n" );
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document.write( "in general log(x) - log(y) = log(x/y)\r<BR>\n" );
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document.write( "your expression becomes:\r<BR>\n" );
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document.write( "log(b,((2y+5)/(y+3)^4))\r<BR>\n" );
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document.write( "to show you how this works, we will let b = 10 because your calculator can do logs to the base of 10 (usually called the LOG function).\r<BR>\n" );
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document.write( "we will let y = 5 (chosen at random small enough to calculate easily).\r<BR>\n" );
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document.write( "your original expression becomes:\r<BR>\n" );
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document.write( "log(2y+5) - 4*log(y+3)\r<BR>\n" );
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document.write( "the base of 10 is implied.\r<BR>\n" );
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document.write( "substituting 5 for y, we get:\r<BR>\n" );
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document.write( "log(2*5+5) - 4*log(5+3) which becomes:\r<BR>\n" );
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document.write( "log(15) - 4*log(8) which becomes -2.436268689\r<BR>\n" );
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document.write( "looking at our final expression of:\r<BR>\n" );
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document.write( "log(b,(2y+5)/(y+3)^4), we get:\r<BR>\n" );
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document.write( "log((2y+5)/(y+3)^4).\r<BR>\n" );
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document.write( "the base of 10 is implied.\r<BR>\n" );
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document.write( "substituting 5 for y, we get:\r<BR>\n" );
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document.write( "log(15/8^4) which becomes log(15/4096).\r<BR>\n" );
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document.write( "using our calculator, we get log(15/4096) = log(.003662109) which equals -2.436268689\r<BR>\n" );
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document.write( "we get the same answer either way, so the translation is good, and the answer to your question is:\r<BR>\n" );
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document.write( "log(b,2y+5) - 4*log(b,y+3) = log(b,(2y+5)/(y+3)^4)  which looks like:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%282y%2B5%29%29+-+4%2Alog%28b%2C%28y%2B3%29%29+=+log%28b%2C%28%282y%2B5%29%2F%28y%2B3%29%5E4%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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