document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1153085>Question 1153085</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the value of ab if https://imgur.com/a/1u4d55h </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #775243 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=775243\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%288%2Ca%29%2Blog%284%2Cb%5E2%29+=+5 ALIGN=MIDDLE  ALT=\"log%288%2Ca%29%2Blog%284%2Cb%5E2%29+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%288%2Cb%29%2Blog%284%2Ca%5E2%29+=+7 ALIGN=MIDDLE  ALT=\"log%288%2Cb%29%2Blog%284%2Ca%5E2%29+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Change the bases of each logarithm, knowing that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E2=4 ALIGN=MIDDLE  ALT=\"2%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E3=8 ALIGN=MIDDLE  ALT=\"2%5E3=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29log%282%2Ca%29%2B%281%2F2%29log%282%2Cb%5E2%29+=+5 ALIGN=MIDDLE  ALT=\"%281%2F3%29log%282%2Ca%29%2B%281%2F2%29log%282%2Cb%5E2%29+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29log%282%2Cb%29%2B%281%2F2%29log%282%2Ca%5E2%29+=+7 ALIGN=MIDDLE  ALT=\"%281%2F3%29log%282%2Cb%29%2B%281%2F2%29log%282%2Ca%5E2%29+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Simplify using the exponent rule of logarithms.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29log%282%2Ca%29%2Blog%282%2Cb%29+=+5 ALIGN=MIDDLE  ALT=\"%281%2F3%29log%282%2Ca%29%2Blog%282%2Cb%29+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29log%282%2Cb%29%2Blog%282%2Ca%29+=+7 ALIGN=MIDDLE  ALT=\"%281%2F3%29log%282%2Cb%29%2Blog%282%2Ca%29+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Change the two equations to exponential form.  (See below for an alternative method for solving the problem from this point.)<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%281%2F3%29%2Ab+=+2%5E5 ALIGN=MIDDLE  ALT=\"a%5E%281%2F3%29%2Ab+=+2%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E%281%2F3%29%2Aa+=+2%5E7 ALIGN=MIDDLE  ALT=\"b%5E%281%2F3%29%2Aa+=+2%5E7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Multiply the two equations together:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28ab%29%5E%284%2F3%29+=+2%5E12 ALIGN=MIDDLE  ALT=\"%28ab%29%5E%284%2F3%29+=+2%5E12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ab+=+2%5E9+=+512 ALIGN=MIDDLE  ALT=\"ab+=+2%5E9+=+512\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: ab = 512<br><BR>\n" );
document.write( "It's more work; but you could also solve the problem by using elimination to solve the pair of equations in the two unknowns, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Ca%29 ALIGN=MIDDLE  ALT=\"log%282%2Ca%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Cb%29 ALIGN=MIDDLE  ALT=\"log%282%2Cb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3log%282%2Cb%29%2Blog%282%2Ca%29+=+15 ALIGN=MIDDLE  ALT=\"3log%282%2Cb%29%2Blog%282%2Ca%29+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29log%282%2Cb%29%2Blog%282%2Ca%29+=+7 ALIGN=MIDDLE  ALT=\"%281%2F3%29log%282%2Cb%29%2Blog%282%2Ca%29+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2F3%29log%282%2Cb%29+=+8 ALIGN=MIDDLE  ALT=\"%288%2F3%29log%282%2Cb%29+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Cb%29+=+3 ALIGN=MIDDLE  ALT=\"log%282%2Cb%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+2%5E3+=+8 ALIGN=MIDDLE  ALT=\"b+=+2%5E3+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3log%282%2Ca%29%2Blog%282%2Cb%29+=+21 ALIGN=MIDDLE  ALT=\"3log%282%2Ca%29%2Blog%282%2Cb%29+=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29log%282%2Ca%29%2Blog%282%2Cb%29+=+5 ALIGN=MIDDLE  ALT=\"%281%2F3%29log%282%2Ca%29%2Blog%282%2Cb%29+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2F3%29log%282%2Ca%29+=+16 ALIGN=MIDDLE  ALT=\"%288%2F3%29log%282%2Ca%29+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Ca%29+=+6 ALIGN=MIDDLE  ALT=\"log%282%2Ca%29+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+2%5E6+=+64 ALIGN=MIDDLE  ALT=\"a+=+2%5E6+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );