document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=818767>Question 818767</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove that, 7log16/15+5log25/24+3log81/80=log2. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #492815 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=492815\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note: In the future please put parentheses around function arguments.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7log%28%2816%2F15%29%29%2B5log%28%2825%2F24%29%29%2B3log%28%2881%2F80%29%29=log%28%282%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "What we will be doing is using properties of logarithms (<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;\" >, <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;\" > and/or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2Alog%28a%2C+%28p%29%29+=+log%28a%2C+%28p%5En%29%29 ALIGN=MIDDLE  ALT=\"n%2Alog%28a%2C+%28p%29%29+=+log%28a%2C+%28p%5En%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) to condense the entire left side into a single logarithm (hopefully log(2)).<br><BR>\n" );
document.write( "We'll start by using the third property to move the coefficients of each log into its argument as its exponent:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28%2816%2F15%29%5E7%29%29%2Blog%28%28%2825%2F24%29%5E5%29%29%2Blog%28%28%2881%2F80%29%5E3%29%29=log%28%282%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Next we can use the first property to combine the three logs:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28%28%2816%2F15%29%5E7%29%2A%28%2825%2F24%29%5E5%29%2A%28%2881%2F80%29%5E3%29%29%29%29=log%28%282%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To make simplifying the argument easier, I am going to rewrite each numerator and denominator in terms of prime factors:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28%28%282%5E4%2F%283%2A5%29%29%5E7%29%2A%28%285%5E2%2F%282%5E3%2A3%29%29%5E5%29%2A%28%283%5E4%2F%282%5E4%2A5%29%29%5E3%29%29%29%29=log%28%282%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we can use the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Fb%29%5En+=+a%5En%2Fb%5En ALIGN=MIDDLE  ALT=\"%28a%2Fb%29%5En+=+a%5En%2Fb%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" > rule to raise each of these fractions to a power:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28%282%5E28%2F%283%5E7%2A5%5E7%29%29%2A%285%5E10%2F%282%5E15%2A3%5E5%29%29%2A%283%5E12%2F%282%5E12%2A5%5E3%29%29%29%29=log%28%282%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5En+%2A+a%5Em+=+a%5E%28n%2Bm%29 ALIGN=MIDDLE  ALT=\"a%5En+%2A+a%5Em+=+a%5E%28n%2Bm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > rule to multiply the numerators and denominators:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28%282%5E28%2A5%5E10%2A3%5E12%29%2F%283%5E12%2A5%5E10%2A2%5E27%29%29%29=log%28%282%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The 3's and 5's all cancel out. And we can use the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5En%2Fa%5Em+=+a%5E%28n-m%29 ALIGN=MIDDLE  ALT=\"a%5En%2Fa%5Em+=+a%5E%28n-m%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > rule to divide the 2's:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%282%5E%2828-27%29%29%29=log%28%282%29%29%29 ALIGN=MIDDLE  ALT=\"log%28%282%5E%2828-27%29%29%29=log%28%282%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%282%5E1%29%29=log%28%282%29%29%29 ALIGN=MIDDLE  ALT=\"log%28%282%5E1%29%29=log%28%282%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%282%29%29=log%28%282%29%29%29 ALIGN=MIDDLE  ALT=\"log%28%282%29%29=log%28%282%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Check! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );