document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=288343>Question 288343</A>: <I><SPAN STYLE=\"word-break: break-all;\"> express as a single logarithm:<BR>\n" );
document.write( "log[6](18)+log[6](48)-2log[6](2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #209020 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=209020\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your expression is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C18%29+%2B+log%286%2C48%29+-+2%2Alog%286%2C2%29 ALIGN=MIDDLE  ALT=\"log%286%2C18%29+%2B+log%286%2C48%29+-+2%2Alog%286%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since, in general, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Alog%28y%29+=+log%28y%5Ex%29 ALIGN=MIDDLE  ALT=\"x%2Alog%28y%29+=+log%28y%5Ex%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C18%29+%2B+log%286%2C48%29+-+2%2Alog%286%2C2%29 ALIGN=MIDDLE  ALT=\"log%286%2C18%29+%2B+log%286%2C48%29+-+2%2Alog%286%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C18%29+%2B+log%286%2C48%29+-+log%286%2C2%5E2%29 ALIGN=MIDDLE  ALT=\"log%286%2C18%29+%2B+log%286%2C48%29+-+log%286%2C2%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C18%29+%2B+log%286%2C48%29+-+log%286%2C4%29 ALIGN=MIDDLE  ALT=\"log%286%2C18%29+%2B+log%286%2C48%29+-+log%286%2C4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since, in general, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%29+-+log%28y%29+=+log%28x%2Fy%29 ALIGN=MIDDLE  ALT=\"log%28x%29+-+log%28y%29+=+log%28x%2Fy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C18%29+%2B+log%286%2C48%29+-+log%286%2C4%29 ALIGN=MIDDLE  ALT=\"log%286%2C18%29+%2B+log%286%2C48%29+-+log%286%2C4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C18%29+%2B+log%286%2C%2848%2F4%29%29 ALIGN=MIDDLE  ALT=\"log%286%2C18%29+%2B+log%286%2C%2848%2F4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C18%29+%2B+log%286%2C%2812%29%29 ALIGN=MIDDLE  ALT=\"log%286%2C18%29+%2B+log%286%2C%2812%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since, in general, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%29+%2B+log%28y%29+=+log%28x%2Ay%29 ALIGN=MIDDLE  ALT=\"log%28x%29+%2B+log%28y%29+=+log%28x%2Ay%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C18%29+%2B+log%286%2C%2812%29%29 ALIGN=MIDDLE  ALT=\"log%286%2C18%29+%2B+log%286%2C%2812%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C%2818%2A12%29%29 ALIGN=MIDDLE  ALT=\"log%286%2C%2818%2A12%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C216%29 ALIGN=MIDDLE  ALT=\"log%286%2C216%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "That's your answer:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C18%29+%2B+log%286%2C48%29+-+2%2Alog%286%2C2%29 ALIGN=MIDDLE  ALT=\"log%286%2C18%29+%2B+log%286%2C48%29+-+2%2Alog%286%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C216%29 ALIGN=MIDDLE  ALT=\"log%286%2C216%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The original expression has been confirmed to be equivalent to the final expression.\r<BR>\n" );
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document.write( "You can check this yourself by using the log function of your calculator.\r<BR>\n" );
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document.write( "The conversion formula to use is that, in general, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2Cx%29+=+log%2810%2Cx%29%2Flog%2810%2C6%29 ALIGN=MIDDLE  ALT=\"log%286%2Cx%29+=+log%2810%2Cx%29%2Flog%2810%2C6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "I will do the original expression for you and then you can do the final expression.\r<BR>\n" );
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document.write( "The original expression is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C18%29+%2B+log%286%2C48%29+-+2%2Alog%286%2C2%29 ALIGN=MIDDLE  ALT=\"log%286%2C18%29+%2B+log%286%2C48%29+-+2%2Alog%286%2C2%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/plot-formula.mpl?expression=log%286%2C18%29+=+log%2810%2C18%29%2Flog%2810%2C6%29+=+1.255272505%2F.77815125+=+1.613147193 ALIGN=MIDDLE  ALT=\"log%286%2C18%29+=+log%2810%2C18%29%2Flog%2810%2C6%29+=+1.255272505%2F.77815125+=+1.613147193\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C48%29+=+log%2810%2C48%29%2Flog%2810%2C6%29+=+1.681241237%2F.77815125+=+2.160558422 ALIGN=MIDDLE  ALT=\"log%286%2C48%29+=+log%2810%2C48%29%2Flog%2810%2C6%29+=+1.681241237%2F.77815125+=+2.160558422\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Alog%286%2C2%29+=+2%2Alog%2810%2C2%29%2Flog%2810%2C6%29+=+2%2A.301029996%2F.77815125+=+.602059991%2F.77815125+=+.773705614 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Plug these values into the original expression equation and you get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C18%29+%2B+log%286%2C48%29+-+2%2Alog%286%2C2%29 ALIGN=MIDDLE  ALT=\"log%286%2C18%29+%2B+log%286%2C48%29+-+2%2Alog%286%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.613147193 + 2.160558422 - .773705614 = 3.\r<BR>\n" );
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document.write( "When you confirm the final expression of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C216%29 ALIGN=MIDDLE  ALT=\"log%286%2C216%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you should also get 3.\r<BR>\n" );
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document.write( "You can convert the log base 6 to log base 10 using the conversion formula shown below:\r<BR>\n" );
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document.write( "Log base 10 is found by using the LOG function of your calculator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C216%29 ALIGN=MIDDLE  ALT=\"log%286%2C216%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C216%29%2Flog%2810%2C6%29 ALIGN=MIDDLE  ALT=\"log%2810%2C216%29%2Flog%2810%2C6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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