document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=104689>Question 104689</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could someone please assist me by solving this logarithmic equation step-by-step for future reference. Thank you.\r<BR>\n" );
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document.write( "log(7y + 1) = 2log(y+3)-log2\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #76196 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=76196\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Some rules to remember <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+log+%28x%29=log%28%28x%5Ek%29%29 ALIGN=MIDDLE  ALT=\"k+log+%28x%29=log%28%28x%5Ek%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28x%29%29%2Blog%28%28y%29%29=log%28%28xy%29%29 ALIGN=MIDDLE  ALT=\"log%28%28x%29%29%2Blog%28%28y%29%29=log%28%28xy%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28x%29%29-log%28%28y%29%29=log%28%28x%2Fy%29%29 ALIGN=MIDDLE  ALT=\"log%28%28x%29%29-log%28%28y%29%29=log%28%28x%2Fy%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "Now let's look at your example.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%287y+%2B+1%29%29+=+2log%28%28y%2B3%29%29-log%28%282%29%29 ALIGN=MIDDLE  ALT=\"log%28%287y+%2B+1%29%29+=+2log%28%28y%2B3%29%29-log%28%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%287y+%2B+1%29%29+-+2log%28%28y%2B3%29%29=+-log%28%282%29%29 ALIGN=MIDDLE  ALT=\"log%28%287y+%2B+1%29%29+-+2log%28%28y%2B3%29%29=+-log%28%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Bring the variable expressions to one side. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%287y+%2B+1%29%29+-+log%28%28y%2B3%29%5E2%29=+log%28%282%5E%28-1%29%29%29 ALIGN=MIDDLE  ALT=\"log%28%287y+%2B+1%29%29+-+log%28%28y%2B3%29%5E2%29=+log%28%282%5E%28-1%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Power rule from above both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28%287y+%2B+1%29%2F%28y%2B3%29%5E2%29%29=+log%28%282%5E%28-1%29%29%29 ALIGN=MIDDLE  ALT=\"log%28%28%287y+%2B+1%29%2F%28y%2B3%29%5E2%29%29=+log%28%282%5E%28-1%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Division rule from above.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287y+%2B+1%29%2F%28y%2B3%29%5E2=+1%2F2 ALIGN=MIDDLE  ALT=\"%287y+%2B+1%29%2F%28y%2B3%29%5E2=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Inverse function both sides. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%287y+%2B+1%29=%28y%2B3%29%5E2 ALIGN=MIDDLE  ALT=\"2%287y+%2B+1%29=%28y%2B3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%28y%2B3%29%5E2 ALIGN=MIDDLE  ALT=\"2%2A%28y%2B3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14y%2B2=y%5E2%2B6y%2B9 ALIGN=MIDDLE  ALT=\"14y%2B2=y%5E2%2B6y%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and expand. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-8y%2B7=0 ALIGN=MIDDLE  ALT=\"y%5E2-8y%2B7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >Group all terms on one side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-1%29%28y-7%29=0 ALIGN=MIDDLE  ALT=\"%28y-1%29%28y-7%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=7 ALIGN=MIDDLE  ALT=\"y=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Two solutions. <BR>\n" );
document.write( "Verify your answer<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%287y+%2B+1%29%29+=+2log%28%28y%2B3%29%29-log%28%282%29%29 ALIGN=MIDDLE  ALT=\"log%28%287y+%2B+1%29%29+=+2log%28%28y%2B3%29%29-log%28%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%287%281%29+%2B+1%29%29+=+2log%28%281%2B3%29%29-log%28%282%29%29 ALIGN=MIDDLE  ALT=\"log%28%287%281%29+%2B+1%29%29+=+2log%28%281%2B3%29%29-log%28%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%288%29%29=2log%28%284%29%29-log%28%282%29%29 ALIGN=MIDDLE  ALT=\"log%28%288%29%29=2log%28%284%29%29-log%28%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%288%29%29=log%28%284%5E2%2F2%29%29 ALIGN=MIDDLE  ALT=\"log%28%288%29%29=log%28%284%5E2%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Power and division rule, right hand side. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%288%29%29=log%28%288%29%29 ALIGN=MIDDLE  ALT=\"log%28%288%29%29=log%28%288%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Good answer. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%287y+%2B+1%29%29+=+2log%28%28y%2B3%29%29-log%28%282%29%29 ALIGN=MIDDLE  ALT=\"log%28%287y+%2B+1%29%29+=+2log%28%28y%2B3%29%29-log%28%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%287%287%29+%2B+1%29%29+=+2log%28%287%2B3%29%29-log%28%282%29%29 ALIGN=MIDDLE  ALT=\"log%28%287%287%29+%2B+1%29%29+=+2log%28%287%2B3%29%29-log%28%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%2850%29%29=2log%28%2810%29%29-log%28%282%29%29 ALIGN=MIDDLE  ALT=\"log%28%2850%29%29=2log%28%2810%29%29-log%28%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%2850%29%29=log%28%2810%5E2%2F2%29%29 ALIGN=MIDDLE  ALT=\"log%28%2850%29%29=log%28%2810%5E2%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Power and division rule, right hand side. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%2850%29%29=log%28%2850%29%29 ALIGN=MIDDLE  ALT=\"log%28%2850%29%29=log%28%2850%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Good answer.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );