document.write( "Question 560393: \"+x%5E%282%28logx%29%5E2%29=10x%5E3+\" \n" ); document.write( "
Algebra.Com's Answer #363875 by Edwin McCravy(20086)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "                  x2[log(x)]² = 10x3\r\n" );
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document.write( "Take logs of both sides:\r\n" );
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document.write( "             log{x2[log(x)]²} = log(10x3)\r\n" );
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document.write( "Use rules of logarithms:\r\n" );
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document.write( "        2[log(x)]²·log(x) = log(10) + log(x³)\r\n" );
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document.write( "               2[log(x)]³ = 1 + 3·log(x)\r\n" );
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document.write( "2[log(x)]³ - 3·log(x) - 1 = 0\r\n" );
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document.write( "let u = log(x)\r\n" );
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document.write( "             2u³ - 3u - 1 = 0\r\n" );
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document.write( "Possible rational solutions for u are ±1, ±\"1%2F2\"\r\n" );
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document.write( "Try 1:\r\n" );
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document.write( "1|2  0 -3 -1\r\n" );
document.write( " |   2  2 -1\r\n" );
document.write( "  2  2 -1 -2 \r\n" );
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document.write( "No that isn't a solution, since it did not give a remainder of 0.\r\n" );
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document.write( "Try -1:\r\n" );
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document.write( "-1|2  0 -3 -1\r\n" );
document.write( "  |  -2  2  1\r\n" );
document.write( "   2 -2 -1  0 \r\n" );
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document.write( "Yes -1 is a solution, so we have factored\r\n" );
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document.write( "             2u³ - 2u - 1 = 0\r\n" );
document.write( "as\r\n" );
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document.write( "     (u + 1)(2u² - 2u - 1) = 0\r\n" );
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document.write( "   u + 1 = 0    2u² - 2u - 1 = 0\r\n" );
document.write( "       u = -1             u = \"%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"\r\n" );
document.write( "                          u = \"%28-%28-2%29+%2B-+sqrt%28%28-2%29%5E2-4%2A%282%29%2A%28-1%29+%29%29%2F%282%2A%282%29%29+\"\r\n" );
document.write( "                          u = \"%282+%2B-+sqrt%284%2B8+%29%29%2F4+\"\r\n" );
document.write( "                          u = \"%282+%2B-+sqrt%2812%29%29%2F4+\"\r\n" );
document.write( "                          u = \"%282+%2B-+2sqrt%283%29%29%2F4+\"\r\n" );
document.write( "                          u = \"%282%281+%2B-+sqrt%283%29%29%29%2F4+\"\r\n" );
document.write( "                          u = \"%281+%2B-+sqrt%283%29%29%2F2+\"\r\n" );
document.write( "                          \r\n" );
document.write( "The log equation u = log(x) is equivalent to the exponential\r\n" );
document.write( "equation x = 10u\r\n" );
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document.write( "So we have three solutions:\r\n" );
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document.write( "x = 10-1, x = \"+matrix%282%2C1%2C%22%22%2C10%5E%28%28%281%2Bsqrt%283%29%29%2F2%29%29%29%29\", x = \"+matrix%282%2C1%2C%22%22%2C10%5E%28%28%281-sqrt%283%29%29%2F2%29%29%29%29\"\r\n" );
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document.write( "In decimal approximations they are\r\n" );
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document.write( "x = 0.1,  x = 23.22872667,  x = 0.4305014278\r\n" );
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document.write( "Edwin
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