document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=143992>Question 143992</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2816%2C%28x%29%29%2Blog%288%2C%28x%29%29%2Blog%284%2C%28x%29%29%2Blog%282%2C%28x%29%29=6 ALIGN=MIDDLE  ALT=\"log%2816%2C%28x%29%29%2Blog%288%2C%28x%29%29%2Blog%284%2C%28x%29%29%2Blog%282%2C%28x%29%29=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #104805 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=104805\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2816%2C%28x%29%29%2Blog%288%2C%28x%29%29%2Blog%284%2C%28x%29%29%2Blog%282%2C%28x%29%29=6 ALIGN=MIDDLE  ALT=\"log%2816%2C%28x%29%29%2Blog%288%2C%28x%29%29%2Blog%284%2C%28x%29%29%2Blog%282%2C%28x%29%29=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%28x%29%29%2Flog%2810%2C%2816%29%29%2Blog%2810%2C%28x%29%29%2Flog%2810%2C%288%29%29%2Blog%2810%2C%28x%29%29%2Flog%2810%2C%284%29%29%2Blog%2810%2C%28x%29%29%2Flog%2810%2C%282%29%29+=+6 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Use the change of base formula to rewrite each individual log. Remeber the change of base formula is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28x%29%29=log%2810%2C%28x%29%29%2Flog%2810%2C%28b%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28x%29%29=log%2810%2C%28x%29%29%2Flog%2810%2C%28b%29%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%2810%2C%28x%29%29%2Flog%2810%2C%282%5E4%29%29%2Blog%2810%2C%28x%29%29%2Flog%2810%2C%282%5E3%29%29%2Blog%2810%2C%28x%29%29%2Flog%2810%2C%282%5E2%29%29%2Blog%2810%2C%28x%29%29%2Flog%2810%2C%282%29%29+=+6 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite 16 as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E4 ALIGN=MIDDLE  ALT=\"2%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Rewrite 8 as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E3 ALIGN=MIDDLE  ALT=\"2%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Rewrite 4 as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E2 ALIGN=MIDDLE  ALT=\"2%5E2\"   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%2810%2C%28x%29%29%2F%284%2Alog%2810%2C%282%29%29%29%2Blog%2810%2C%28x%29%29%2F%283%2Alog%2810%2C%282%29%29%29%2Blog%2810%2C%28x%29%29%2F%282%2Alog%2810%2C%282%29%29%29%2Blog%2810%2C%28x%29%29%2Flog%2810%2C%282%29%29+=+6 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the each denominator using the identity  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%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=24%2Alog%2810%2C%282%29%29%2A%28log%2810%2C%28x%29%29%2Fcross%284%2Alog%2810%2C%282%29%29%29%2Blog%2810%2C%28x%29%29%2Fcross%283%2Alog%2810%2C%282%29%29%29%2Blog%2810%2C%28x%29%29%2Fcross%282%2Alog%2810%2C%282%29%29%29%2Blog%2810%2C%28x%29%29%2Fcross%28log%2810%2C%282%29%29%29%29+=24%2Alog%2810%2C%282%29%29%2A%286%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Alog%2810%2C%282%29%29 ALIGN=MIDDLE  ALT=\"24%2Alog%2810%2C%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Doing this will eliminate the denominators.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Alog%2810%2C%28x%29%29%2B8%2Alog%2810%2C%28x%29%29%2B12%2Alog%2810%2C%28x%29%29%2B24%2Alog%2810%2C%28x%29%29=144%2Alog%2810%2C%282%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%28x%29%29%286%2B8%2B12%2B24%29=144%2Alog%2810%2C%282%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%28x%29%29%286%2B8%2B12%2B24%29=144%2Alog%2810%2C%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%28x%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%28x%29%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%2810%2C%28x%29%29%2850%29=144%2Alog%2810%2C%282%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%28x%29%29%2850%29=144%2Alog%2810%2C%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50%2Alog%2810%2C%28x%29%29=144%2Alog%2810%2C%282%29%29 ALIGN=MIDDLE  ALT=\"50%2Alog%2810%2C%28x%29%29=144%2Alog%2810%2C%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%28x%5E50%29%29=log%2810%2C%282%5E144%29%29 ALIGN=MIDDLE  ALT=\"log%2810%2C%28x%5E50%29%29=log%2810%2C%282%5E144%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the expressions using the identity  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Alog%28b%2C%28x%29%29=log%28b%2C%28x%5Ey%29%29 ALIGN=MIDDLE  ALT=\"y%2Alog%28b%2C%28x%29%29=log%28b%2C%28x%5Ey%29%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=x%5E50=2%5E144 ALIGN=MIDDLE  ALT=\"x%5E50=2%5E144\"   DISABLED_style= \"max-width:90%; height:auto;\" > Since the logs have the same base, this means that the argument (the terms inside the log) are equal.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=root%2850%2C2%5E144%29 ALIGN=MIDDLE  ALT=\"x=root%2850%2C2%5E144%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the 50th root of both sides\r<BR>\n" );
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document.write( "So our answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=root%2850%2C2%5E144%29 ALIGN=MIDDLE  ALT=\"x=root%2850%2C2%5E144%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7.361501 ALIGN=MIDDLE  ALT=\"x=7.361501\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "note: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=root%2850%2C2%5E144%29 ALIGN=MIDDLE  ALT=\"x=root%2850%2C2%5E144%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be written as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=root%2850%2C2%5E144%29 ALIGN=MIDDLE  ALT=\"x=root%2850%2C2%5E144%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 2^{\frac{144}{50}}=2^{\frac{72}{25}}\"> </SPAN>\n" );
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