document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174002>Question 174002</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you write the expression as a single logarithum:<BR>\n" );
document.write( "1/2[log(base4)(x+1) + 2log(base4)(x-1)] +6log(base4)(x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #128939 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=128939\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is:<BR>\n" );
document.write( "1/2[log(base4)(x+1) + 2log(base4)(x-1)] +6log(base4)(x)<BR>\n" );
document.write( "this looks to me like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2A%28%28log%284%2Cx%2B1%29%29+%2B+%282%2Alog%284%2Cx-1%29%29%29+%2B+6%2Alog%284%2Cx%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you have a couple of concepts to work with:<BR>\n" );
document.write( "these are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2Ca%29+%2B+log%284%2Cb%29+=+log%284%2Ca%2Ab%29 ALIGN=MIDDLE  ALT=\"log%284%2Ca%29+%2B+log%284%2Cb%29+=+log%284%2Ca%2Ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2Alog%284%2Ca%29+=+log%284%2Ca%5Ec%29 ALIGN=MIDDLE  ALT=\"c%2Alog%284%2Ca%29+=+log%284%2Ca%5Ec%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we will remove the inner parentheses first and work outwards.<BR>\n" );
document.write( "you have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Alog%284%2Cx-1%29 ALIGN=MIDDLE  ALT=\"2%2Alog%284%2Cx-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2C%28x-1%29%5E2%29 ALIGN=MIDDLE  ALT=\"log%284%2C%28x-1%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "working our way outwards, you have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2Cx%2B1%29+%2B+log%284%2C%28x-1%29%5E2%29 ALIGN=MIDDLE  ALT=\"log%284%2Cx%2B1%29+%2B+log%284%2C%28x-1%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2C%28x%2B1%29%2A%28x-1%29%5E2%29 ALIGN=MIDDLE  ALT=\"log%284%2C%28x%2B1%29%2A%28x-1%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "working our way outwards again, you have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2A%28log%284%2C%28x%2B1%29%2A%28x-1%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%2A%28log%284%2C%28x%2B1%29%2A%28x-1%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2C%28%28x%2B1%29%2A%28x-1%29%5E2%29%5E%281%2F2%29%29 ALIGN=MIDDLE  ALT=\"log%284%2C%28%28x%2B1%29%2A%28x-1%29%5E2%29%5E%281%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we now have in total:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2C%28%28x%2B1%29%2A%28x-1%29%5E2%29%5E%281%2F2%29%29+%2B+6%2Alog%284%2Cx%29 ALIGN=MIDDLE  ALT=\"log%284%2C%28%28x%2B1%29%2A%28x-1%29%5E2%29%5E%281%2F2%29%29+%2B+6%2Alog%284%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Alog%284%2Cx%29+=+log%284%2Cx%5E2%29 ALIGN=MIDDLE  ALT=\"6%2Alog%284%2Cx%29+=+log%284%2Cx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so we have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2C%28%28x%2B1%29%2A%28x-1%29%5E2%29%5E%281%2F2%29%29+%2B+log%284%2Cx%5E6%29 ALIGN=MIDDLE  ALT=\"log%284%2C%28%28x%2B1%29%2A%28x-1%29%5E2%29%5E%281%2F2%29%29+%2B+log%284%2Cx%5E6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%284%2C%28%28%28x%2B1%29%2A%28x-1%29%5E2%29%5E%281%2F2%29%2Ax%5E6%29%29 ALIGN=MIDDLE  ALT=\"log%284%2C%28%28%28x%2B1%29%2A%28x-1%29%5E2%29%5E%281%2F2%29%2Ax%5E6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "i checked the answer and it appears to be good.<BR>\n" );
document.write( "i did this by solving both equations for a given value of x.<BR>\n" );
document.write( "i used x = 2.<BR>\n" );
document.write( "i got the same answer both ways (the original equation and the condensed equation).<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you can solve this as well if you wish to prove the answer is good.<BR>\n" );
document.write( "you can use your calculator by converting to base 10 as follows:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log4%2Cx%29+=+log%2810%2Cx%29%2Flog%2810%2C4%29 ALIGN=MIDDLE  ALT=\"log4%2Cx%29+=+log%2810%2Cx%29%2Flog%2810%2C4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );