document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=279144>Question 279144</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If log2=0.3010 and log3=0.4771, find the value of :<BR>\n" );
document.write( "7 log 10/9 -2 log 25/24 +3 log 31/80 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #203292 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=203292\">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=7log%28%2810%2F9%29%29+-2log%28%2825%2F24%29%29+%2B+3log%28%2831%2F80%29%29 ALIGN=MIDDLE  ALT=\"7log%28%2810%2F9%29%29+-2log%28%2825%2F24%29%29+%2B+3log%28%2831%2F80%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I don't think the problem can be done without a calculator with that 31 in there. So I am going to assume that the 31 should be an 81 instead:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7log%28%2810%2F9%29%29+-2log%28%2825%2F24%29%29+%2B+3log%28%2881%2F80%29%29 ALIGN=MIDDLE  ALT=\"7log%28%2810%2F9%29%29+-2log%28%2825%2F24%29%29+%2B+3log%28%2881%2F80%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I am going to start by factor the numbers in the arguments into prime factors:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7log%28%28%282%2A5%29%2F3%5E2%29%29+-2log%28%285%5E2%2F%282%5E3%2A3%29%29%29+%2B+3log%28%283%5E4%2F%282%5E4%2A5%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Next I'll use the property of logarithms, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%2Alog%28a%2C+%28p%29%29+=+log%28a%2C+%28p%5Eq%29%29 ALIGN=MIDDLE  ALT=\"q%2Alog%28a%2C+%28p%29%29+=+log%28a%2C+%28p%5Eq%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to move the coefficients of the logarithms into the arguments as exponents:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28%28%282%2A5%29%2F3%5E2%29%5E7%29%29+-log%28%28%285%5E2%2F%282%5E3%2A3%29%29%5E2%29%29+%2B+log%28%28%283%5E4%2F%282%5E4%2A5%29%29%5E3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using rules for exponents in the argument to simplify we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28%282%5E7%2A5%5E7%29%2F3%5E14%29%29+-log%28%285%5E4%2F%282%5E6%2A3%5E2%29%29%29+%2B+log%28%283%5E12%2F%282%5E12%2A5%5E3%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Next I'll use the properties of logarithms:<ul><li><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2C+%28p%29%29+%2B+log%28a%2C+%28q%29%29+=+log%28a%2C+%28p%2Aq%29%29 ALIGN=MIDDLE  ALT=\"log%28a%2C+%28p%29%29+%2B+log%28a%2C+%28q%29%29+=+log%28a%2C+%28p%2Aq%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></li><li><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2C+%28p%29%29+-+log%28a%2C+%28q%29%29+=+log%28a%2C+%28p%2Fq%29%29 ALIGN=MIDDLE  ALT=\"log%28a%2C+%28p%29%29+-+log%28a%2C+%28q%29%29+=+log%28a%2C+%28p%2Fq%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></li></ul><BR>\n" );
document.write( "to combine the three logarithms into one:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28+%282%5E7%2A5%5E7%2A3%5E12%29%2F%28%28%283%5E14%29%285%5E4%29%282%5E12%2A5%5E3%29%29%2F%282%5E6%2A3%5E2%29%29+%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we simplify this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28+%282%5E7%2A5%5E7%2A3%5E12%2A%282%5E6%2A3%5E2%29%29%2F%28%283%5E14%29%285%5E4%29%282%5E12%2A5%5E3%29%29+%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28+%282%5E13%2A5%5E7%2A3%5E14%29%2F%283%5E14%2A5%5E7%2A2%5E12%29+%29%29 ALIGN=MIDDLE  ALT=\"log%28%28+%282%5E13%2A5%5E7%2A3%5E14%29%2F%283%5E14%2A5%5E7%2A2%5E12%29+%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28+2+%29%29 ALIGN=MIDDLE  ALT=\"log%28%28+2+%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which, by the information you've been given is 0.3010 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );