document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=155459>Question 155459</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Describe how to obtain the third answer in each row from the first two questions?\r<BR>\n" );
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document.write( "a) log [base 8]512, log [base 2] 512,log [base 16] 512<BR>\n" );
document.write( "b) log [base 4]64, log [base 8]64, log [base 32]64\r<BR>\n" );
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document.write( "I don't know how they got the third answer for these two sequences. Can you show the steps on how you got the third answer? This way I can understand. Thank you for all the hard work!! Also, I don't know which ISBN to put because my question isn't from a textbook. Sorry!<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #114511 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=114511\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, you recall that the definition of the logarithm of a numer is:<BR>\n" );
document.write( "\"The logarithm of a number is the power to which the base of the logarithm must be raised to equal the number\"<BR>\n" );
document.write( "a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Log%5B16%5D%28512%29+=+x ALIGN=MIDDLE  ALT=\"Log%5B16%5D%28512%29+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" > so, by the above definition, x is the power to which 16 (the base) must be raised to equal the number (512). So you can write that out as described:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%5Ex+=+512 ALIGN=MIDDLE  ALT=\"16%5Ex+=+512\"   DISABLED_style= \"max-width:90%; height:auto;\" > The next step is to exprees the the numbers on both sides as powers of the same base.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16+=+2%5E4 ALIGN=MIDDLE  ALT=\"16+=+2%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=512+=+2%5E9 ALIGN=MIDDLE  ALT=\"512+=+2%5E9\"   DISABLED_style= \"max-width:90%; height:auto;\" > so make the appropriate substitutions to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%284x%29+=+2%5E9 ALIGN=MIDDLE  ALT=\"2%5E%284x%29+=+2%5E9\"   DISABLED_style= \"max-width:90%; height:auto;\" > now since the bases (2) are equal, the exponents are equal, so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+=+9 ALIGN=MIDDLE  ALT=\"4x+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+9%2F4 ALIGN=MIDDLE  ALT=\"x+=+9%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Log%5B16%5D%28512%29+=+9%2F4 ALIGN=MIDDLE  ALT=\"Log%5B16%5D%28512%29+=+9%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Log%5B16%5D%28512%29+=+2.25 ALIGN=MIDDLE  ALT=\"Log%5B16%5D%28512%29+=+2.25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Similarly:<BR>\n" );
document.write( "b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Log%5B32%5D%2864%29+=+x ALIGN=MIDDLE  ALT=\"Log%5B32%5D%2864%29+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32%5Ex+=+64 ALIGN=MIDDLE  ALT=\"32%5Ex+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" > but<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32+=+2%5E5 ALIGN=MIDDLE  ALT=\"32+=+2%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64+=+2%5E6 ALIGN=MIDDLE  ALT=\"64+=+2%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E5x+=+2%5E6 ALIGN=MIDDLE  ALT=\"2%5E5x+=+2%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x+=+6 ALIGN=MIDDLE  ALT=\"5x+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and..<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+6%2F5 ALIGN=MIDDLE  ALT=\"x+=+6%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > then...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Log%5B16%5D%2864%29+=+6%2F5 ALIGN=MIDDLE  ALT=\"Log%5B16%5D%2864%29+=+6%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Log%5B16%5D%2864%29+=+1.2 ALIGN=MIDDLE  ALT=\"Log%5B16%5D%2864%29+=+1.2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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