document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=114268>Question 114268</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0495013579/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> (2/3)log_x512=2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #83162 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=83162\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If I interpret your problem correctly it is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29%2Alog%28x%2C512%29+=+2 ALIGN=MIDDLE  ALT=\"%282%2F3%29%2Alog%28x%2C512%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Since the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29 ALIGN=MIDDLE  ALT=\"%282%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a multiplier of the log function, by the rules of logarithms it<BR>\n" );
document.write( "can be taken inside as an exponent of the quantity on which the log is operating. <BR>\n" );
document.write( "In other words an equivalent equation is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%2C512%5E%282%2F3%29%29+=+2 ALIGN=MIDDLE  ALT=\"log%28x%2C512%5E%282%2F3%29%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now let's calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=512%5E%282%2F3%29 ALIGN=MIDDLE  ALT=\"512%5E%282%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28512%5E2%29%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"%28512%5E2%29%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is <BR>\n" );
document.write( "equivalent to the cube root of 512 squared. Calculator time ... when you square 512 you<BR>\n" );
document.write( "get 262144. And when you take the cube root of 262144 you get 64. So in the equation you<BR>\n" );
document.write( "can replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=512%5E%282%2F3%29 ALIGN=MIDDLE  ALT=\"512%5E%282%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64 ALIGN=MIDDLE  ALT=\"64\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%2C64%29+=+2 ALIGN=MIDDLE  ALT=\"log%28x%2C64%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now convert this from logarithmic form to exponential form. The rule is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2Cb%29+=+y ALIGN=MIDDLE  ALT=\"log%28a%2Cb%29+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to the exponential form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Ey+=+b ALIGN=MIDDLE  ALT=\"a%5Ey+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "By comparing this rule to the equation we have, we can say that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%2C64%29+=+2 ALIGN=MIDDLE  ALT=\"log%28x%2C64%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to the exponential form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+64 ALIGN=MIDDLE  ALT=\"x%5E2+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Take the square root of both sides of the equivalent exponential form and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+sqrt%2864%29+=+8 ALIGN=MIDDLE  ALT=\"x+=+sqrt%2864%29+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "so the base of the logarithm that makes the given problem true is 8 and you can write<BR>\n" );
document.write( "the original problem statement as:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29%2Alog%288%2C512%29+=+2 ALIGN=MIDDLE  ALT=\"%282%2F3%29%2Alog%288%2C512%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to understand the problem. <BR>\n" );
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document.write( " </SPAN>\n" );
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