document.write( "Question 79558This question is from textbook College Algebra Graphs and Models
\n" ); document.write( ": I am trying to figure out this question. ln(x+1)= ln(3x+1)-ln x??? I keep getting x= square root 2x+1. but I don't think that is write??? I am horrible at these. Please help!!! \n" ); document.write( "
Algebra.Com's Answer #57099 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "         ln(x+1) = ln(3x+1) - ln x\r\n" );
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document.write( " ln(x+1) + ln(x) = ln(3x+1)\r\n" );
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document.write( "      ln[(x+1)x] = ln(3x+1)\r\n" );
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document.write( "        ln(x²+x) = ln(3x+1)\r\n" );
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document.write( "Use the rule:  if ln(A) = ln(B) then A = B\r\n" );
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document.write( "            x²+x = 3x+1\r\n" );
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document.write( "     x² - 2x - 1 = 0\r\n" );
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document.write( "Get 0 on the right by subtracting 3x and 1 \r\n" );
document.write( "from both sides:\r\n" );
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document.write( "     x² - 2x - 1 = 0\r\n" );
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document.write( "Use the quadratic formula:\r\n" );
document.write( "                  ______ \r\n" );
document.write( "            -b ± Öb²-4ac\r\n" );
document.write( "        x = —————————————\r\n" );
document.write( "                2a \r\n" );
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document.write( "where a = 1; b = -2; c = -1\r\n" );
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document.write( "                      ______________\r\n" );
document.write( "             -(-2) ± Ö(-2)²-4(1)(-1)\r\n" );
document.write( "        x = ————————————————————————\r\n" );
document.write( "                     2(1) \r\n" );
document.write( "                  ___ \r\n" );
document.write( "             2 ± Ö4+4\r\n" );
document.write( "        x = ———————————\r\n" );
document.write( "                 2\r\n" );
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document.write( "                  _ \r\n" );
document.write( "             2 ± Ö8\r\n" );
document.write( "        x = ————————\r\n" );
document.write( "                2 \r\n" );
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document.write( "                  ___ \r\n" );
document.write( "             2 ± Ö4·2\r\n" );
document.write( "        x = ———————————\r\n" );
document.write( "                 2 \r\n" );
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document.write( "                   _ \r\n" );
document.write( "             2 ± 2Ö2\r\n" );
document.write( "        x = ——————————\r\n" );
document.write( "                2 \r\n" );
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document.write( "                     _\r\n" );
document.write( "             2     2Ö2\r\n" );
document.write( "        x = ——— ± —————\r\n" );
document.write( "             2      2\r\n" );
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document.write( "        x = 1 ± Ö2 \r\n" );
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document.write( "Using the +, x = 1 + Ö2, which\r\n" );
document.write( "is one answer and equals about 2.141213562\r\n" );
document.write( "                      _ \r\n" );
document.write( "Using the -, x = 1 - Ö2, which\r\n" );
document.write( "is the other answer and equals about -.4142135624.\r\n" );
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document.write( "However since the original problem contains ln(x), \r\n" );
document.write( "and since logarithms can only be taken of positive \r\n" );
document.write( "numbers, the only solution is:\r\n" );
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document.write( " x = 1 + Ö2  \r\n" );
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document.write( "Edwin
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