document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1148576>Question 1148576</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, this is a logarithmic problem. I need a step by step explanation of:<BR>\n" );
document.write( "16^log4(8). I know the answer is 64, but I need to show my work.<BR>\n" );
document.write( "Is it possible to solve this problem by rewriting 16 as 2^4 and log 4 as 2^2 and 8 as 2^3. If so, please explain<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 #769908 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=769908\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "There are many variations of how to simplify this expression.  The method you are asking about is one of them.  Here is how it might go....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%5Elog%284%2C8%29 ALIGN=MIDDLE  ALT=\"16%5Elog%284%2C8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Rewriting each number as a power of 2....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%5E4%29%5E%28log%282%5E2%2C2%5E3%29%29 ALIGN=MIDDLE  ALT=\"%282%5E4%29%5E%28log%282%5E2%2C2%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now in the exponent <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28log%282%5E2%2C2%5E3%29%29 ALIGN=MIDDLE  ALT=\"%28log%282%5E2%2C2%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > you can use the \"change of base formula\"<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2Ca%29=+log%28n%2Ca%29%2Flog%28n%2Cb%29 ALIGN=MIDDLE  ALT=\"log%28b%2Ca%29=+log%28n%2Ca%29%2Flog%28n%2Cb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "and choose n=2 as the base:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28log%282%2C2%5E3%29%2F%28log%282%2C2%5E2%29%29%29+=+3%2F2 ALIGN=MIDDLE  ALT=\"%28log%282%2C2%5E3%29%2F%28log%282%2C2%5E2%29%29%29+=+3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So now the expression is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%5E4%29%5E%283%2F2%29+=+2%5E%284%2A%283%2F2%29%29+=+2%5E6+=+64 ALIGN=MIDDLE  ALT=\"%282%5E4%29%5E%283%2F2%29+=+2%5E%284%2A%283%2F2%29%29+=+2%5E6+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );