document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=704768>Question 704768</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i have to use logrithms to solve the folowing equation, correct to 4 significant figures 4=32(1-2x) the brackets are small if that makes a diference\r<BR>\n" );
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document.write( "please tell me how you got to your answer  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #434252 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=434252\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The part \"correct to 4 significant figures\" must have come from general instructions given for a test including many questions.<BR>\n" );
document.write( "The instructions may have included using logarithms as needed, but logarithms are not needed to solve that equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=32%281-2x%29 ALIGN=MIDDLE  ALT=\"4=32%281-2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=32%2A1-32%2A2x ALIGN=MIDDLE  ALT=\"4=32%2A1-32%2A2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > applying the distributive property<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=32%2A1-32%2A2x ALIGN=MIDDLE  ALT=\"4=32%2A1-32%2A2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=32-64x ALIGN=MIDDLE  ALT=\"4=32-64x\"   DISABLED_style= \"max-width:90%; height:auto;\" > performing indicated multiplications<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=32-64x ALIGN=MIDDLE  ALT=\"4=32-64x\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2B64x-4=32-64x%2B64x-4 ALIGN=MIDDLE  ALT=\"4%2B64x-4=32-64x%2B64x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64x-4 ALIGN=MIDDLE  ALT=\"64x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides of the equal sign<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2B64x-4=32-64x%2B64x-4 ALIGN=MIDDLE  ALT=\"4%2B64x-4=32-64x%2B64x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64x%2B4-4=32-64x%2B64x-4 ALIGN=MIDDLE  ALT=\"64x%2B4-4=32-64x%2B64x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64x=32-4 ALIGN=MIDDLE  ALT=\"64x=32-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64x=28 ALIGN=MIDDLE  ALT=\"64x=28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "rearranging (commutative and associative properties) and doing indicated operations<BR>\n" );
document.write( "The explanation for that step could get even more involved, if you wanted<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64x=28 ALIGN=MIDDLE  ALT=\"64x=28\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64x%2F64=28%2F64 ALIGN=MIDDLE  ALT=\"64x%2F64=28%2F64\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=28%2F64 ALIGN=MIDDLE  ALT=\"x=28%2F64\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7%2F8 ALIGN=MIDDLE  ALT=\"x=7%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I do not need a calculator, or a slide rule, or logarithms to divide 7 by 8 to find the answer as a decimal.<BR>\n" );
document.write( "I can calculate that in my head, without even paper and pencil, thinking this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F8=1-1%2F8=1-1%2A125%2F%288%2A125%29=1-125%2F1000=1-0.1250000=0.8750000 ALIGN=MIDDLE  ALT=\"7%2F8=1-1%2F8=1-1%2A125%2F%288%2A125%29=1-125%2F1000=1-0.1250000=0.8750000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "USING LOGARITHMS:<BR>\n" );
document.write( "I have not needed to use logarithms to divide since calculators were invented.<BR>\n" );
document.write( "(I hope you are not expected to do that)<BR>\n" );
document.write( "If it was a more complicated fraction/division, and I only had a table of base 10 logarithms, paper, and pencil, I would calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F8 ALIGN=MIDDLE  ALT=\"7%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a decimal correct to 4 significant figures like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%287%2F8%29=log%287%29+-+log+%288%29=0.8450980-0.9030900=-0.0579920=-1%2B1-0.0579920=-1%2B0.9420080 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then, I would look in the table for the number that has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.9420080 ALIGN=MIDDLE  ALT=\"0.9420080\"   DISABLED_style= \"max-width:90%; height:auto;\" > for a logarithm.<BR>\n" );
document.write( "I would see that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%288.74%29=0.9415114 ALIGN=MIDDLE  ALT=\"log%288.74%29=0.9415114\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%288.75%29=0.9420081 ALIGN=MIDDLE  ALT=\"log%288.75%29=0.9420081\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%288.76%29=0.9425041 ALIGN=MIDDLE  ALT=\"log%288.76%29=0.9425041\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since the difference between consecutive logs is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%288.75%29-log%288.74%29=0.0004967 ALIGN=MIDDLE  ALT=\"log%288.75%29-log%288.74%29=0.0004967\"   DISABLED_style= \"max-width:90%; height:auto;\" > for numbers differing in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.01 ALIGN=MIDDLE  ALT=\"0.01\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "if would not even try to interpolate to get a more accurate answer,<BR>\n" );
document.write( "because I would figure (without even calculating it), that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%288.749%29=0.9420081-0.01%2A0.000497=0.9420081-%280.001%2F0.01%29%2A0.0000497=0.9419584 ALIGN=MIDDLE  ALT=\"log%288.749%29=0.9420081-0.01%2A0.000497=0.9420081-%280.001%2F0.01%29%2A0.0000497=0.9419584\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is much farther than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%288.750%29 ALIGN=MIDDLE  ALT=\"log%288.750%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.9420080 ALIGN=MIDDLE  ALT=\"0.9420080\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=0.8750%29 ALIGN=MIDDLE  ALT=\"highlight%28x=0.8750%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an answer correct to 4 significant figures. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );