document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134465>Question 1134465</A>: <I><SPAN STYLE=\"word-break: break-all;\"> pls help me with this, log27 base x + log4 base y = 5 ; log27 base x - log4 base y = 1. find x and y </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #751854 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=751854\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> looks like you are solving two equations simultaneouosly with the twist that they involve logs.\r<BR>\n" );
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document.write( "the two equations are:\r<BR>\n" );
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document.write( "log27(x) + log4(y) = 5<BR>\n" );
document.write( "log27(x) - log4(y) = 1\r<BR>\n" );
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document.write( "subtract the second equation from the first to get:\r<BR>\n" );
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document.write( "2 * log4(y) = 4\r<BR>\n" );
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document.write( "divide both sides of this equation by 2 to get log4(y) = 2\r<BR>\n" );
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document.write( "since log4(y) = 2, then both equations become:\r<BR>\n" );
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document.write( "log27(x) + 2 = 5<BR>\n" );
document.write( "log27(x) - 2 = 1\r<BR>\n" );
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document.write( "add these two equations together to get:\r<BR>\n" );
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document.write( "2 * log27(x) = 6\r<BR>\n" );
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document.write( "divide this equaion by 2 to get log27(x) = 3.\r<BR>\n" );
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document.write( "your solution so far is:\r<BR>\n" );
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document.write( "log27(x) + log4(y) = 5 which becomes 3 + 2 = 5<BR>\n" );
document.write( "log27(x) - log4(y) = 1 which becomes 3 - 2 = 1\r<BR>\n" );
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document.write( "the equations have been solved simultaneously and what is left is to find the value of x and y.\r<BR>\n" );
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document.write( "it was already determined that log27(x) = 3 and log4(y) = 2.\r<BR>\n" );
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document.write( "log27(x) = 3 if and only if 27^3 = x.<BR>\n" );
document.write( "this makes x = 19683.\r<BR>\n" );
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document.write( "log4(y) = 2 if and only if 4^2 = y.<BR>\n" );
document.write( "this makes y = 16.\r<BR>\n" );
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document.write( "your solution is that x = 19683 and y = 16.\r<BR>\n" );
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document.write( "you can confirm by using the base log conversion formula and your calculator.\r<BR>\n" );
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document.write( "log27(19683) = log(19683) / log(27) = 3\r<BR>\n" );
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document.write( "log4(16) = log(16) / log(4) = 2\r<BR>\n" );
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document.write( "solution is confirmed to be good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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