document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=965036>Question 965036</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I solve these problems?\r<BR>\n" );
document.write( "\n" );
document.write( "1.  log(2 - x) = 0.5\r<BR>\n" );
document.write( "\n" );
document.write( "2.  log(x + 25) = log(x + 10) + log 4  <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #589816 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=589816\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the first one is solved as follows:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "log(2-x) = .5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is true if and only 10^.5 = 2-x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "square both sides of this equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "10 = (2-x)^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "10 = 4 - 4x + x^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract 10 from both sides and re-arrange the terms to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x^2 - 4x - 6 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "factor using the quadratic formula to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 5.16227766\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = -1.16227766\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "both values work.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "just replace them in the original equation and you'll see.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the second problem is solved as follows:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "log(x + 25) = log(x + 10) + log 4  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is equivalent to log(x + 25) = log(4 * (x + 10) which is equivalent to log(x + 25) = log(4x + 40).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is true if and only if x + 25 = 4x + 40\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for x to get x = -5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "replace x with -5 in the original equation and you'll see that they're equivalent.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "log(-5 + 25) = log(20).\\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "log(x + 10) + log(4) is equal to log(5) + log(4) which is equal to log(5 * 4) which is equal to log(20).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the rule of logs that are used are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "logb(x) = y if and only if b^y = x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "logb(a) + logb(b) = logb(a * b)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );