document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=369496>Question 369496</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the logarithmic equation algebraically. Round to three decimal places.\r<BR>\n" );
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document.write( "log base(4)5x- log(4)(6+sq root of x)=2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #263358 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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=263358\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve the logarithmic equation algebraically. Round to three decimal places.\r<BR>\n" );
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document.write( "log base(4)5x- log(4)(6+sq root of x)=2\r<BR>\n" );
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document.write( "log4 (5x) - log4 (6 + sqrt(x)) = 2<BR>\n" );
document.write( "logarithmic rule: logb (m/n) = logb (m) - logb (n)<BR>\n" );
document.write( "log4 (5x/(6 + sqrt(x))) = 2<BR>\n" );
document.write( "logarithmic rule: logb (m) = logk (m)/ logk b, where k is your new base<BR>\n" );
document.write( "log4 (5x/(6 + sqrt(x))) = [log10 (5x/(6 + sqrt(x)))] / log10 (4) = 2<BR>\n" );
document.write( "log10 (5x/(6 + sqrt(x))) = 2log10 (4)<BR>\n" );
document.write( "logarithmic rule: nlogb (m) = logb (m^n)<BR>\n" );
document.write( "4^2 = 16<BR>\n" );
document.write( "log10 (5x/(6 + sqrt(x))) = log10 (16)\r<BR>\n" );
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document.write( "5x/(6 + sqrt(x)) = 16<BR>\n" );
document.write( "5x = 16(6 + sqrt(x))<BR>\n" );
document.write( "5x = 96 + 16sqrt(x)<BR>\n" );
document.write( "5x - 96 = 16sqrt(x)<BR>\n" );
document.write( "(5x - 96)^2 = (16sqrt(x))^2 (square both sides)<BR>\n" );
document.write( "25x^2 - 960x + 9216 = 256x<BR>\n" );
document.write( "25x^2 - 1216x + 9216 = 0, solve this and determine which root works\r<BR>\n" );
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document.write( "use quadratic formula, a = 25, b = -1216, c = 9216<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281216+%2B-+sqrt%281478656+-+4%2A25%2A9216%29%29%2F50+ ALIGN=MIDDLE  ALT=\"x+=+%281216+%2B-+sqrt%281478656+-+4%2A25%2A9216%29%29%2F50+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281216+%2B-+sqrt%281478656+-+921600%29%29%2F50+ ALIGN=MIDDLE  ALT=\"x+=+%281216+%2B-+sqrt%281478656+-+921600%29%29%2F50+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281216+%2B-+sqrt%281478656+-+921600%29%29%2F50+ ALIGN=MIDDLE  ALT=\"x+=+%281216+%2B-+sqrt%281478656+-+921600%29%29%2F50+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281216+%2B-+sqrt%28557056%29%29%2F50+ ALIGN=MIDDLE  ALT=\"x+=+%281216+%2B-+sqrt%28557056%29%29%2F50+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "557056 = 128 * 128 * 34<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28608+%2B-+64sqrt%2834%29%29%2F25+ ALIGN=MIDDLE  ALT=\"x+=+%28608+%2B-+64sqrt%2834%29%29%2F25+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "x1 = 608/25 + (64/25)sqrt(34)<BR>\n" );
document.write( "x1 = 24.32 + 2.56sqrt(34)<BR>\n" );
document.write( "x1 = 39.247237 to 6 places = 39.247 to 3 places<BR>\n" );
document.write( "x2 = 24.32 - 2.56sqrt(34)<BR>\n" );
document.write( "x2 = 9.392763 to 6 places = 9.392 to 3 places\r<BR>\n" );
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document.write( "check log10 (5x/(6 + sqrt(x))) = log10 (16)<BR>\n" );
document.write( "log10 (16) = 1.204120 to 6 places<BR>\n" );
document.write( "x1 gives log10 (16) = log10 (16), x1 works<BR>\n" );
document.write( "x2 gives log10 (5.180921) which does not equal log10 (16), x2 does not work\r<BR>\n" );
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document.write( "answer for x is 39.247 to 3 places\r<BR>\n" );
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