document.write( "Question 1209868: If 2^{16^x} = 128*4^x, then find 2^x. \n" ); document.write( "

Algebra.Com's Answer #850937 by ikleyn(52776) $\"\"$ $\"About$

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\n" ); document.write( "If 2^{16^x} = 128*4^x, then find 2^x.
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document.write( "Your starting equation is\r\n" );
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document.write( "    2^{16^x} = 128*4^x.\r\n" );
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document.write( "Notice that 2^(16^x) = 2^(2^(4x)).  \r\n" );
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document.write( "So, the original equation is equivalent to \r\n" );
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document.write( "    2^(2^(4x)) = 2^7 * 2^(2x).\r\n" );
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document.write( "It implies for indexes\r\n" );
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document.write( "    2^(4x) = 2x + 7.\r\n" );
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document.write( "This equation can not be solved algebraically, but it can be solved approximately \r\n" );
document.write( "with reasonable precision using numerical methods and special solvers in the Internet.\r\n" );
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document.write( "I used online solver at the site www.desmos.com/calculator. The calculator produced two approximate solutions\r\n" );
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document.write( "     = -3.49997  (approximately),  and    = 0.77389  (approximately)\r\n" );
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document.write( "            As the reference to the solver' solution, see this link\r\n" );
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document.write( "            https://www.desmos.com/calculator/tmxp2wpqt3\r\n" );
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document.write( "Therefore,   may have two values\r\n" );
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document.write( "     = 0.08839  (approx.)  and    = 1.709874 (approx.)\r\n" );
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document.write( "These values,  = 0.08838  and   = 1.709874,  are your ANSWER  to the problem's question.\r\n" );
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