document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1101530>Question 1101530</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2logx+8=log4<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #716145 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=716145\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this can be interpreted as:\r<BR>\n" );
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document.write( "2 * log(x) + 8 = log(4)\r<BR>\n" );
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document.write( "if so, then:\r<BR>\n" );
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document.write( "subtract 8 from both sides of the equation to get:\r<BR>\n" );
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document.write( "2 * log(x) = log(4) - 8\r<BR>\n" );
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document.write( "since 2 * log(x) is equal to log(x^2), then:\r<BR>\n" );
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document.write( "log(x^2) = log(4) - 8\r<BR>\n" );
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document.write( "by the basic definition of logs, this is true, if and only if:\r<BR>\n" );
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document.write( "10^(log(4)-8) = x^2\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = plus or minus square root of (10^(log(4)-8)\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = plus or minus .0002\r<BR>\n" );
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document.write( "x can't be negative because log(x) can't be negative, therefore x = .0002.\r<BR>\n" );
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document.write( "confirm by replacing x with .0002 in the original equation.\r<BR>\n" );
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document.write( "2 * log(.0002) + 8 = .6020599913<BR>\n" );
document.write( "log(4) = the same.\r<BR>\n" );
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document.write( "solution is confirmed.\r<BR>\n" );
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document.write( "the problem could also be interpreted as:\r<BR>\n" );
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document.write( "2 * log(x+8) = log(4)\r<BR>\n" );
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document.write( "in that case:\r<BR>\n" );
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document.write( "divide both sides of the equation by 2 to get log(x+8) = log(4)/2\r<BR>\n" );
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document.write( "this is true if and only if 10^(log(4)/2) = x+8\r<BR>\n" );
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document.write( "solve for x to get x = 10^(log(4)/2)-8 = -6\r<BR>\n" );
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document.write( "you get x = -6\r<BR>\n" );
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document.write( "replace x in the original equation of 2 * log(x+8) = log(4) with -6 to get:\r<BR>\n" );
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document.write( "2*log(-6+8) = .6020599913<BR>\n" );
document.write( "log(4) = .6020599913\r<BR>\n" );
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document.write( "they're the same so the solution is confirmed to be good.\r<BR>\n" );
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document.write( "it is always good to use parentheses to ensure that what you are asking is interpreted as such by the people you are asking it to.\r<BR>\n" );
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document.write( "you have two possible answers, depending on what your original equation was asking.\r<BR>\n" );
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document.write( "2 * log(x) + 8 = log(4) yields x = .0002\r<BR>\n" );
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document.write( "2 * log(x+8) = log(4) yields x = -6\r<BR>\n" );
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document.write( "the general logarithmic equation properties used are:\r<BR>\n" );
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document.write( "log(x^n) = n*log(x)<BR>\n" );
document.write( "log(x) = y if and only if x = 10^y\r<BR>\n" );
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document.write( "the more general form of the last statement is:\r<BR>\n" );
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document.write( "logb(x) = y if and only if x = b^y\r<BR>\n" );
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document.write( "when you use the form of log(x) without mentioning the base, the base is assumed to be 10.\r<BR>\n" );
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document.write( "the log function of your calculator assumes the base is 10.\r<BR>\n" );
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document.write( "log(x) means the same thing as log10(x).\r<BR>\n" );
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