document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=742292>Question 742292</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve and check<BR>\n" );
document.write( "a) log(3x+2)+log(x-1)=2<BR>\n" );
document.write( "b)2log(x-1)=2+log100\r<BR>\n" );
document.write( "\n" );
document.write( "Can you please help me out? Thanks so much in advance:)<BR>\n" );
document.write( "Can you please show the work it will help me understand better:) thanks again </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #452399 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=452399\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve and check<BR>\n" );
document.write( "a) log(3x+2) + log(x-1) = 2<BR>\n" );
document.write( "Addition of logs means multiply<BR>\n" );
document.write( "log[(3x+2)*(x-1)] = 2<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "log(3x^2 - 3x + 2x - 2) = 2<BR>\n" );
document.write( "log(3x^2 - x - 2) = 2<BR>\n" );
document.write( "exponent equiv of logs<BR>\n" );
document.write( "3x^2 - x - 2 = 10^2<BR>\n" );
document.write( "3x^2 - x - 2 = 100<BR>\n" );
document.write( "3x^2 - x - 2 - 100 = 0<BR>\n" );
document.write( "3x^2 - x - 102 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(3x + 17)(x - 6) = 0<BR>\n" );
document.write( "The positive solution is all we want here<BR>\n" );
document.write( "x = 6<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check this out using a calc<BR>\n" );
document.write( "log(3(6)+2) + log(6-1) = 2<BR>\n" );
document.write( "log(20) + log(5) = 2<BR>\n" );
document.write( "1.3 + .7 = 2; confirms our solution of x=6<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "b)2log(x-1) = 2 + log(100) <BR>\n" );
document.write( "we know the log of 100 is so we can write it<BR>\n" );
document.write( "2log(x-1) = 2 + 2<BR>\n" );
document.write( "2log(x-1) = 4<BR>\n" );
document.write( "log[(x-1)^2] = 4<BR>\n" );
document.write( "Exponent equiv<BR>\n" );
document.write( "(x-1)^2 = 10^4<BR>\n" );
document.write( "(x-1)^2 = 10000<BR>\n" );
document.write( "find the square root of both sides<BR>\n" );
document.write( "x - 1 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2810000%29 ALIGN=MIDDLE  ALT=\"sqrt%2810000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x - 1 = 100<BR>\n" );
document.write( "x = 100 + 1<BR>\n" );
document.write( "x = 101<BR>\n" );
document.write( ":<BR>\n" );
document.write( "I'll let you check this solution, replace x with 101: </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );