document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1034627>Question 1034627</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Evaluate the following expression .\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2log%2810%2C5%2F3%29+ ALIGN=MIDDLE  ALT=\"+2log%2810%2C5%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%2810+%2C+7%2F4%29+ ALIGN=MIDDLE  ALT=\"+log%2810+%2C+7%2F4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2log%2810%2C3%29+ ALIGN=MIDDLE  ALT=\"+2log%2810%2C3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F2%29log%28+10%2C49%29+ ALIGN=MIDDLE  ALT=\"+%281%2F2%29log%28+10%2C49%29+\"   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 #649271 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=649271\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your expression is:\r<BR>\n" );
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document.write( "2log10(5/3) - log10(7/4) + 2log10(3) + (1/2)*log10(49).\r<BR>\n" );
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document.write( "since it's all log10, you can evaluate it as is by using the log function of your calculator.\r<BR>\n" );
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document.write( "you will get:\r<BR>\n" );
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document.write( "2log(5/3) - log(7/4) + 2log(3) + (1/2)*log(49) = 2.\r<BR>\n" );
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document.write( "the log function of your calculator assumes log10, therefore log(x) in the calculator is the same as log10(x).\r<BR>\n" );
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document.write( "you could also simplify it and then evaluate it.\r<BR>\n" );
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document.write( "2log(5/3) is equal to log((5/3)^2) = log(25/9).<BR>\n" );
document.write( "- log(7/4) is equal to - log(7/4).<BR>\n" );
document.write( "2log(3) is equal to log(3^2) = log(9).<BR>\n" );
document.write( "1/2*log(49) is equal to log(49^(1/2)) = log(7).\r<BR>\n" );
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document.write( "the expression becomes:\r<BR>\n" );
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document.write( "log(25/9) - log(7/4) + log(9) + log(7).\r<BR>\n" );
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document.write( "since log(a) - log(b) = log(a/b), and since log(a) + log(b) = log(a*b), you can simplify this expression to get:\r<BR>\n" );
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document.write( "log((25/9*9*7)/(7/4))\r<BR>\n" );
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document.write( "you can simplify this to log(100).\r<BR>\n" );
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document.write( "this is equal to y if and only if 10^y = 100.<BR>\n" );
document.write( "10^y is equal to 100 when y is equal to 2.<BR>\n" );
document.write( "therefore:<BR>\n" );
document.write( "log(100) = 2 </SPAN>\n" );
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