document.write( "Question 1042616: e^4x+5e^2x-24=0 \r
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Algebra.Com's Answer #657604 by ikleyn(52814) $\"\"$ $\"About$

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\n" ); document.write( "e^4x+5e^2x-24=0 \r
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\n" ); document.write( "\n" ); document.write( "There are two ways.\r
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document.write( "1.  Let y =  be a new variable.\r\n" );
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document.write( "    Then your equation can be written in the form\r\n" );
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document.write( "     = 0.\r\n" );
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document.write( "    Factor left side:\r\n" );
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document.write( "    (y + 8)*(y-3) = 0.\r\n" );
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document.write( "    The roots are y = -8 and y = 3.\r\n" );
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document.write( "    Then the original equation deploys in two:\r\n" );
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document.write( "     = -8,  which has no solutions,  and\r\n" );
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document.write( "     = 0, which is equivalent to  = 3  and has the solution  2x = ln(3),  or  x = .\r\n" );
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document.write( "2.  Factor the original equation as\r\n" );
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document.write( "     = .\r\n" );
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document.write( "    Then it deploys in two equations:\r\n" );
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document.write( "     = -8,  which has no solutions,  and\r\n" );
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document.write( "     = 3,  which . . . .    and so on from the n.1 . . . \r\n" );
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\n" ); document.write( "\n" ); document.write( "Introducing new variable is a standard way and it makes the solution as simple as possible.\r
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\n" ); document.write( "\n" ); document.write( "When and if you know this method well, you may apply direct factoring without introducing new variable.\r
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