document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=142348>Question 142348</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the equation : x^a - x^b = z , where 'x' & 'z' is a positive integer, where a>b and 'a' & 'b' are positive integers. Can we find the value of 'a' & 'b' ? when the value of 'z' and 'x' is given. Is there any method.                    For example given eqn 2^a - 2^b = 32512. Here can we find that a=15 and b=8.<BR>\n" );
document.write( "For example given eqn 3^a - 3^b = 6318. Here can we find that a=8 and b=5.<BR>\n" );
document.write( "I need method to find a and b.  This is the question of finding two variables in an equation.  Please help me to know this. If possible please find URL where solution is present.(FROM SHIVA) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #103633 by </B><A HREF=/tutors/aboutme.mpl?userid=scott8148><B>scott8148(6628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=scott8148><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=scott8148><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=103633\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x^a-x^b=x^b[x^(a-b)-1] __ x^(a-b)-1=z/(x^b)\r<BR>\n" );
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document.write( "x^b should be the highest power of x that evenly divides into z\r<BR>\n" );
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document.write( "2^a - 2^b = 32512 __ 2^8(2^(15-8)-1)=32512 __ 2^7-1=127 __ 2^7=128\r<BR>\n" );
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document.write( "3^a - 3^b = 6318 __ 3^5(3^(8-5)-1)=6318 __ 3^3-1=26 __ 3^3=27 </SPAN>\n" );
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