document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203466>Question 203466</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0132329034/algebrahomeworkh>Sullivan College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Write expression as sum/difference of logarithms. Express as powers of factors:  log (sub 2) (a^2 square root of b)^4, a>0, b>0.\r<BR>\n" );
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document.write( "I got this far:  log sub 2 a^8 + log sub 2 (square root of b)^4\r<BR>\n" );
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document.write( "but I'm not even so sure about that.  Can you pls show me how to finish?  THanks!<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 #153497 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=153497\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C+%28a%5E2%2Asqrt%28b%29%29%5E4%29 ALIGN=MIDDLE  ALT=\"log%282%2C+%28a%5E2%2Asqrt%28b%29%29%5E4%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%282%2C+%28a%5E8%29%29+%2B+log%282%2C+%28sqrt%28b%29%5E4%29%29 ALIGN=MIDDLE  ALT=\"log%282%2C+%28a%5E8%29%29+%2B+log%282%2C+%28sqrt%28b%29%5E4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Is good so far. We can simplify the 2nd log by using the fact that a square root is the same as an exponent of 1/2:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C+%28a%5E8%29%29+%2B+log%282%2C+%28%28b%5E%281%2F2%29%29%5E4%29%29 ALIGN=MIDDLE  ALT=\"log%282%2C+%28a%5E8%29%29+%2B+log%282%2C+%28%28b%5E%281%2F2%29%29%5E4%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%282%2C+%28a%5E8%29%29+%2B+log%282%2C+%28b%5E2%29%29 ALIGN=MIDDLE  ALT=\"log%282%2C+%28a%5E8%29%29+%2B+log%282%2C+%28b%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is a sum of logarithms. I'm not sure what \"Express as powers of factors\" means. But I am guessing that the next simplification is desired. We can use the following property of logarithms: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28x%5Ey%29%29+=+y%2Alog%28x%29 ALIGN=MIDDLE  ALT=\"log%28%28x%5Ey%29%29+=+y%2Alog%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This allows us to \"move\" an exponent from the argument \"out in front\":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8log%282%2C+%28a%29%29+%2B+2log%282%2C+%28b%29%29 ALIGN=MIDDLE  ALT=\"8log%282%2C+%28a%29%29+%2B+2log%282%2C+%28b%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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