document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=935990>Question 935990</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28+3%2C+7+%29+%2A+log%28+4%2C+3+%29+%2A+log%28+7%2C+6+%29+ ALIGN=MIDDLE  ALT=\"+log%28+3%2C+7+%29+%2A+log%28+4%2C+3+%29+%2A+log%28+7%2C+6+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >) as a single logarithm. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #569412 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=569412\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this was a doozy, but i think i was able to figure it out.\r<BR>\n" );
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document.write( "by the log conversion formula, you get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C7%29+=+log%287%29%2Flog%283%29 ALIGN=MIDDLE  ALT=\"log%283%2C7%29+=+log%287%29%2Flog%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2C3%29+=+log%283%29%2Flog%284%29 ALIGN=MIDDLE  ALT=\"log%284%2C3%29+=+log%283%29%2Flog%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%2C7%29+=+log%286%29%2Flog%287%29 ALIGN=MIDDLE  ALT=\"log%286%2C7%29+=+log%286%29%2Flog%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you get the following equation:\r<BR>\n" );
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document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28+3%2C+7+%29+%2A+log%28+4%2C+3+%29+%2A+log%28+7%2C+6+%29+ ALIGN=MIDDLE  ALT=\"+log%28+3%2C+7+%29+%2A+log%28+4%2C+3+%29+%2A+log%28+7%2C+6+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%287%29%2Flog%283%29+%2A+log%283%29%2Flog%284%29+%2A+log%286%29%2Flog%287%29 ALIGN=MIDDLE  ALT=\"log%287%29%2Flog%283%29+%2A+log%283%29%2Flog%284%29+%2A+log%286%29%2Flog%287%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%287%29 ALIGN=MIDDLE  ALT=\"log%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the numerator and denominator cancel out, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%29 ALIGN=MIDDLE  ALT=\"log%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the numerator and denominator cancel out and you are left with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%29+%2F+log%284%29 ALIGN=MIDDLE  ALT=\"log%286%29+%2F+log%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "by the log base conversion formula, you get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2C6%29+=+log%286%29+%2F+log%284%29 ALIGN=MIDDLE  ALT=\"log%284%2C6%29+=+log%286%29+%2F+log%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and so your final solution is:\r<BR>\n" );
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document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28+3%2C+7+%29+%2A+log%28+4%2C+3+%29+%2A+log%28+7%2C+6+%29+ ALIGN=MIDDLE  ALT=\"+log%28+3%2C+7+%29+%2A+log%28+4%2C+3+%29+%2A+log%28+7%2C+6+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%284%2C6%29 ALIGN=MIDDLE  ALT=\"+log%284%2C6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "to confirm the solution is correct, you have to go back to the log conversion formulas.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%284%2C6%29 ALIGN=MIDDLE  ALT=\"+log%284%2C6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%286%29%2Flog%284%29 ALIGN=MIDDLE  ALT=\"log%286%29%2Flog%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.29248125.\r<BR>\n" );
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document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28+3%2C+7+%29+%2A+log%28+4%2C+3+%29+%2A+log%28+7%2C+6+%29+ ALIGN=MIDDLE  ALT=\"+log%28+3%2C+7+%29+%2A+log%28+4%2C+3+%29+%2A+log%28+7%2C+6+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%287%29%2Flog%283%29+%2A+log%283%29%2Flog%284%29+%2A+log%286%29%2Flog%287%29 ALIGN=MIDDLE  ALT=\"log%287%29%2Flog%283%29+%2A+log%283%29%2Flog%284%29+%2A+log%286%29%2Flog%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.29248125.\r<BR>\n" );
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document.write( "they give you the same value, so they're equivalent.\r<BR>\n" );
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document.write( "your solution is that the expression becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2C6%29 ALIGN=MIDDLE  ALT=\"log%284%2C6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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