document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=406920>Question 406920</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I find a solution for :\r<BR>\n" );
document.write( "\n" );
document.write( "Log base of 10 4x - log base of 10 (12 + square 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 #288576 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=288576\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Log base of 10 4x - log base of 10 (12 + square root of x) = 2\r<BR>\n" );
document.write( "\n" );
document.write( "..\r<BR>\n" );
document.write( "\n" );
document.write( "log4x-log(12+sqrt(x)=2<BR>\n" );
document.write( "applying division rule,<BR>\n" );
document.write( "log(4x/(12+sqrt(x)=2<BR>\n" );
document.write( "convert to exponential form (the base raised to the logarithm of the number is equal to the number. In this case the base=10, the logarithm of the number=2, and the number is (4x/(12+sqrt(x)) <BR>\n" );
document.write( "4x/(12+sqrt(x)=10^2=100<BR>\n" );
document.write( "4x=1200+100sqrt(x)<BR>\n" );
document.write( "x=300+25sqrt(x)<BR>\n" );
document.write( "x-25sqrt(x)-300=0<BR>\n" );
document.write( "let u=sqrt(x)<BR>\n" );
document.write( "then u^2=x<BR>\n" );
document.write( "u^2-25u-300=0<BR>\n" );
document.write( "using quadratic formula to solve,<BR>\n" );
document.write( "a=1,b=-25,c=-300<BR>\n" );
document.write( "u=-(-25)+-sqrt((-25)^2-4(1)(-300))/2(1)<BR>\n" );
document.write( "u=(25+-sqrt(1825))/2<BR>\n" );
document.write( "u=(25+-42.72)/2<BR>\n" );
document.write( "u=33.86<BR>\n" );
document.write( "u=-8.86 (reject, in log x, x>0<BR>\n" );
document.write( "x=u^2=(33.86)^2=1146.5\r<BR>\n" );
document.write( "\n" );
document.write( "..\r<BR>\n" );
document.write( "\n" );
document.write( "check:<BR>\n" );
document.write( "log4x-log(12+sqrt(x)<BR>\n" );
document.write( "log(4*1146.5)-log(12+sqrt(1146.5)<BR>\n" );
document.write( "log(4586)-log(45.86)<BR>\n" );
document.write( "=3.66-1.66=2=right-hand side\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );