document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=691014>Question 691014</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What am I doing wrong here or am I on the right track?\r<BR>\n" );
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document.write( "log5x - log5(x - 2) = log5 4\r<BR>\n" );
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document.write( "log5x - log5 (x - 2) = log5/log4\r<BR>\n" );
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document.write( "log5 x-(x-2) = 1.161\r<BR>\n" );
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document.write( "-x^2 + 2x - 1.161 = 0\r<BR>\n" );
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document.write( "-b +- sqrt b^2 - 4(a)(c) / 2(a)\r<BR>\n" );
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document.write( "-2 +- sqrt 2^2 - 4(-1)(-1.161) / 2(-1)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #426470 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=426470\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Unfortunately, you are far from the right track, and trouble rendering the notation does not help.<BR>\n" );
document.write( "I believe the problem is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%285%2Cx%29+-+log%285%2C%28x+-+2%29%29+=+log%285%2C+4%29 ALIGN=MIDDLE  ALT=\"log%285%2Cx%29+-+log%285%2C%28x+-+2%29%29+=+log%285%2C+4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For such a problem, you should know and use the definition and properties of logarithms (see below).<BR>\n" );
document.write( " <BR>\n" );
document.write( "THE SOLUTION:<BR>\n" );
document.write( "Using knowledge about logarithms:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%285%2Cx%29-log%285%2C%28x-2%29%29=log%285%2C4%29 ALIGN=MIDDLE  ALT=\"log%285%2Cx%29-log%285%2C%28x-2%29%29=log%285%2C4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%2F%28x-2%29%29=log%285%2C4%29 ALIGN=MIDDLE  ALT=\"log%28x%2F%28x-2%29%29=log%285%2C4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28x-2%29=4 ALIGN=MIDDLE  ALT=\"x%2F%28x-2%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28x-2%29=4 ALIGN=MIDDLE  ALT=\"x%2F%28x-2%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2F%28x-2%29%29%28x-2%29=4%28x-2%29 ALIGN=MIDDLE  ALT=\"%28x%2F%28x-2%29%29%28x-2%29=4%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4x-8 ALIGN=MIDDLE  ALT=\"x=4x-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-x=4x-8-x ALIGN=MIDDLE  ALT=\"x-x=4x-8-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=3x-8 ALIGN=MIDDLE  ALT=\"0=3x-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-8=0 ALIGN=MIDDLE  ALT=\"3x-8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-8%2B8=0%2B8 ALIGN=MIDDLE  ALT=\"3x-8%2B8=0%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=8 ALIGN=MIDDLE  ALT=\"3x=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2F3=8%2F3 ALIGN=MIDDLE  ALT=\"3x%2F3=8%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=8%2F3%29 ALIGN=MIDDLE  ALT=\"highlight%28x=8%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " <BR>\n" );
document.write( "DEFINITION:<BR>\n" );
document.write( "Logarithm of a number is defined (in down to earth terms) as the exponent you need to put on the base to get that number.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%285%2C25%29=2 ALIGN=MIDDLE  ALT=\"log%285%2C25%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%285%2C125%29=3 ALIGN=MIDDLE  ALT=\"log%285%2C125%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25=5%5E2 ALIGN=MIDDLE  ALT=\"25=5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=125=5%5E3 ALIGN=MIDDLE  ALT=\"125=5%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%285%2C4%29 ALIGN=MIDDLE  ALT=\"log%285%2C4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not such a simple number.<BR>\n" );
document.write( "You cannot write its exact value as a fraction or a decimal, but it's approximately 0.8614.<BR>\n" );
document.write( " <BR>\n" );
document.write( "PROPERTTIES OF LOGARITHMS:<BR>\n" );
document.write( "Some teachers may give you formulas for the properties of logarithms and expect you to remember them.<BR>\n" );
document.write( "However, it is easy to remember (or rediscover) most of those properties by thinking from the definition of logarithm.<BR>\n" );
document.write( "SUM OF LOGARITHMS:<BR>\n" );
document.write( "When using the same base, multiplying powers means adding the exponents<BR>\n" );
document.write( "(example <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E4%29%28x%5E5%29=x%5E9 ALIGN=MIDDLE  ALT=\"%28x%5E4%29%28x%5E5%29=x%5E9\"   DISABLED_style= \"max-width:90%; height:auto;\" >).<BR>\n" );
document.write( "So, when logarithms of the same base are added, you get the logarithm of the product.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2Cx%29%2Blog%28b%2Cy%29=log%28b%2Cxy%29 ALIGN=MIDDLE  ALT=\"log%28b%2Cx%29%2Blog%28b%2Cy%29=log%28b%2Cxy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "DIFFERENCE OF LOGARITHMS:<BR>\n" );
document.write( "Similarly, subtracting logarithms of the same base gives you the logarithm of the quotient.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2Cx%29-log%28b%2Cy%29=log%28b%2Cx%2Fy%29 ALIGN=MIDDLE  ALT=\"log%28b%2Cx%29-log%28b%2Cy%29=log%28b%2Cx%2Fy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "CHANGE OF BASE:<BR>\n" );
document.write( "That is not quite so obvious.<BR>\n" );
document.write( "To calculate the approximate value of the logarithm of a number in a strange base (like 5), you divide the base 10 logarithms of the number by the base 10 logarithms of the strange base.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2Cx%29=log%2810%2Cx%29%2Flog%2810%2Cb%29 ALIGN=MIDDLE  ALT=\"log%28b%2Cx%29=log%2810%2Cx%29%2Flog%2810%2Cb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%285%2C4%29=log%2810%2C4%29%2Flog%2810%2C5%29 ALIGN=MIDDLE  ALT=\"log%285%2C4%29=log%2810%2C4%29%2Flog%2810%2C5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and since the base can be omitted is it is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you can write it as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%285%2C4%29=log%284%29%2Flog%285%29 ALIGN=MIDDLE  ALT=\"log%285%2C4%29=log%284%29%2Flog%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );