document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1062603>Question 1062603</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the value of x if: log5 + log(x+2) - log(x-1) = 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #677561 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=677561\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> start with:\r<BR>\n" );
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document.write( "log(5) + log(x+2) - log(x-1) = 2\r<BR>\n" );
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document.write( "subtract log(5) from both sides to get:\r<BR>\n" );
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document.write( "log(x+2) - log(x-1) = 2 - log(5)\r<BR>\n" );
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document.write( "since log(2) = 100, this becomes:\r<BR>\n" );
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document.write( "log(x+2) - log(x-1) = log(100) - log(5)\r<BR>\n" );
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document.write( "this is equivalent to:\r<BR>\n" );
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document.write( "log((x+2)/(x-1)) = log(100/5) which is equal to:\r<BR>\n" );
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document.write( "log((x+2)/(x-1)) = log(20)\r<BR>\n" );
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document.write( "this is true if and only if (x+2)/(x-1) = 20\r<BR>\n" );
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document.write( "solve for x to get x = 22/19.\r<BR>\n" );
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document.write( "replace x with 22/19 in your original equation and you will see that the equation is true.\r<BR>\n" );
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document.write( "you will get log(5) + log(60/19) - log(3/19) = 2\r<BR>\n" );
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document.write( "evaluate this using your calculator to get 2 = 2.\r<BR>\n" );
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document.write( "this confirms your solution is correct.\r<BR>\n" );
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document.write( "your solution is x = 22/19.\r<BR>\n" );
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