document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=27408>Question 27408</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I was wondering if you could perhapse teach me how to solve this question step by step. thank you.\r<BR>\n" );
document.write( "\n" );
document.write( "Solve for b.\r<BR>\n" );
document.write( "\n" );
document.write( "logb(1/512)= -3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #14876 by </B><A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.com><B>sdmmadam@yahoo.com(530)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.com><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=14876\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  I was wondering if you could perhapse teach me how to solve this question step by step. thank you. <BR>\n" );
document.write( "Solve for b. <BR>\n" );
document.write( "logb(1/512)= -3\r<BR>\n" );
document.write( "\n" );
document.write( "The definition of the logarithm of a non zero number N to a given base b <BR>\n" );
document.write( "is defined as the power p  to which the base b has to be raised to give <BR>\n" );
document.write( "the number N<BR>\n" );
document.write( "That is logb(N) = p means b^p = N<BR>\n" );
document.write( "Using this definition,<BR>\n" );
document.write( "logb(1/512)= -3<BR>\n" );
document.write( "gives b^(-3) = 1/512<BR>\n" );
document.write( "That is 1/b^3 = 1/8^3  (using y^(-n) = 1/y^n )<BR>\n" );
document.write( "which implies b^3 = 8^3<BR>\n" );
document.write( "which gives b=8 (powers are equal and hence bases are equal)<BR>\n" );
document.write( "Answer: b=8 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );