document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=295203>Question 295203</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I found this question in book entitled 1001 solved problems in engineering math, the book already gives the answer but i dont understand how it is done,here is the question:<BR>\n" );
document.write( "(a^n)(a^m)=100000<BR>\n" );
document.write( "(a^n)/(a^m)=10<BR>\n" );
document.write( "find the value of a:<BR>\n" );
document.write( "I hope it will be answered with some explanation in it. thank you for the help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #212787 by </B><A HREF=/tutors/aboutme.mpl?userid=dabanfield><B>dabanfield(803)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=dabanfield><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=212787\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I found this question in book entitled 1001 solved problems in engineering math, the book already gives the answer but i dont understand how it is done,here is the question:<BR>\n" );
document.write( "(a^n)(a^m)=100000<BR>\n" );
document.write( "(a^n)/(a^m)=10<BR>\n" );
document.write( "find the value of a:\r<BR>\n" );
document.write( "\n" );
document.write( "a^n*a^m = 100000<BR>\n" );
document.write( "a^(n+m) = 100000<BR>\n" );
document.write( "log a^(n+m) = log 10^5<BR>\n" );
document.write( "(n+m)*log a = 5<BR>\n" );
document.write( "1.) n*log a + m*log a = 5\r<BR>\n" );
document.write( "\n" );
document.write( "a^n/a^m = 1<BR>\n" );
document.write( "a^(n-m) = 10^1<BR>\n" );
document.write( "log a^(n-m) = log 10^1<BR>\n" );
document.write( "(n-m)*log a = 1<BR>\n" );
document.write( "2.) n*log a - m*log a = 1\r<BR>\n" );
document.write( "\n" );
document.write( "Adding 1.) and 2.) we have:\r<BR>\n" );
document.write( "\n" );
document.write( "2*n*log a = 6<BR>\n" );
document.write( "n*log a = 3<BR>\n" );
document.write( "n = 3/log a\r<BR>\n" );
document.write( "\n" );
document.write( "Substituting 3/log a for n in 2.):\r<BR>\n" );
document.write( "\n" );
document.write( "((3/log a)*log a) - m*log a = 1<BR>\n" );
document.write( "3 - m*log a = 1<BR>\n" );
document.write( "m*log a = 2<BR>\n" );
document.write( "m = 2/log a\r<BR>\n" );
document.write( "\n" );
document.write( "Since a*(n-m) = 10\r<BR>\n" );
document.write( "\n" );
document.write( "(n-m)*log a = 1<BR>\n" );
document.write( "log a = 1/(n-m)<BR>\n" );
document.write( "log a = 1/((3/log a - 2/log a))<BR>\n" );
document.write( "log a = 1/log a<BR>\n" );
document.write( "(log a)^2 = 1<BR>\n" );
document.write( "log a = +sqrt(1) or -sqrt(1)<BR>\n" );
document.write( "log a = 1 or log a = -1\r<BR>\n" );
document.write( "\n" );
document.write( "By definition of a log then:<BR>\n" );
document.write( "a = 10 or a = 1/10\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );