document.write( "Question 1210448: Solve 24(2²ˣ) - 5(2ˣ⁺²) - 156 = 0, where x ∈ R
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Algebra.Com's Answer #852556 by ikleyn(53354) $\"\"$ $\"About$

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document.write( "This given equation\r\n" );
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document.write( "     -    - 156  =  0    (1)\r\n" );
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document.write( "is the same as\r\n" );
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document.write( "      -    -  156  =  0,\r\n" );
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document.write( "or\r\n" );
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document.write( "     -  -  156  =  0.    (2)\r\n" );
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document.write( "Introduce new variable  y = .\r\n" );
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document.write( "Then equation (2)  takes the form\r\n" );
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document.write( "     -  - 156 = 0,\r\n" );
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document.write( "and we are looking for positive solutions to this equation.\r\n" );
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document.write( "Apply the quadratic formula and get the solutions to equation (2)\r\n" );
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document.write( "    y = 3  and  y = -13/6.\r\n" );
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document.write( "Only positive solution y = 3 does fit.\r\n" );
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document.write( "So, for x we have\r\n" );
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document.write( "     = 3,   hence,  x =  = 1.584962501  (approximately).\r\n" );
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document.write( "ANSWER.  x =  = 1.584962501  (approximately).\r\n" );
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\n" ); document.write( "\n" ); document.write( "This is a standard problem to solve exponential equation by introducing new variable.\r
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