document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=712639>Question 712639</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 123 base b =83 solve for b. \r<BR>\n" );
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document.write( "I would be happy if someone could even just show me the steps, please. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #438095 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=438095\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In general, to convert from base b to base 10, you plug the digits a0...an from left to right into the polynomial of the form a0*b^n + ... an*b^0\r<BR>\n" );
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document.write( "So that would mean\r<BR>\n" );
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document.write( "<font color=\"red\">x</font><font color=\"blue\">y</font><font color=\"green\">z</font> base b = <font color=\"red\">x</font>*b^2 + <font color=\"blue\">y</font>*b^1 + <font color=\"green\">z</font>*b^0\r<BR>\n" );
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document.write( "<font color=\"red\">1</font><font color=\"blue\">2</font><font color=\"green\">3</font> base b = <font color=\"red\">1</font>*b^2 + <font color=\"blue\">2</font>*b^1 + <font color=\"green\">3</font>*b^0\r<BR>\n" );
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document.write( "123 base b = 1*b^2 + 2*b^1 + 3*b^0\r<BR>\n" );
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document.write( "123 base b = 1*b^2 + 2*b + 3*b^0\r<BR>\n" );
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document.write( "83 = 1*b^2 + 2*b + 3*b^0\r<BR>\n" );
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document.write( "1*b^2 + 2*b + 3*b^0 = 83\r<BR>\n" );
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document.write( "b^2 + 2b + 3 = 83\r<BR>\n" );
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document.write( "b^2 + 2b + 3 - 83 = 0\r<BR>\n" );
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document.write( "b^2 + 2b - 80 = 0\r<BR>\n" );
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document.write( "(b+10)(b-8) = 0\r<BR>\n" );
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document.write( "b+10 = 0 or b-8 = 0\r<BR>\n" );
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document.write( "b = -10 or b = 8\r<BR>\n" );
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document.write( "Toss out the negative base\r<BR>\n" );
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document.write( "The only solution left is b = 8\r<BR>\n" );
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document.write( "So 123 base <font color=\"red\">8</font> = 83 base 10\r<BR>\n" );
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document.write( " </SPAN>\n" );
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