document.write( "Question 1147557: Using suitable substitutions solve for x, 2e^x=7√e^x -3 \n" ); document.write( "
Algebra.Com's Answer #768892 by ikleyn(52799)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            Look into your post, please, as it came to the forum.\r
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\n" ); document.write( "\n" ); document.write( "            From the post, it is UNCLEAR how far the square root symbol is spreading to the right.\r
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document.write( "If your equation is   \r\n" );
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document.write( "    \"2%2Ae%5Ex\" = \"7%2Asqrt%28e%5Ex%29\" - 3      (1)\r\n" );
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document.write( "then the solution is as follows.\r\n" );
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document.write( "Introduce new variable  u = \"sqrt%28e%5Ex%29\".\r\n" );
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document.write( "Then the equation (1) takes the form\r\n" );
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document.write( "    \"2u%5E2\" = 7*u - 3\r\n" );
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document.write( "    \"2u%5E2+-+7u+%2B+3\" = 0\r\n" );
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document.write( "    (2u-1)*(u-3) = 0\r\n" );
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document.write( "Case 1.  2u - 1 = 0\r\n" );
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document.write( "                 u = \"1%2F2\"\r\n" );
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document.write( "                \"sqrt%28e%5Ex%29\" = \"1%2F2\"\r\n" );
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document.write( "                \"e%5Ex\" = \"1%2F4\"\r\n" );
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document.write( "                x = \"ln%281%2F4%29\" = -2*ln(2).  \r\n" );
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document.write( "                It is the answer for Case 1.\r\n" );
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document.write( "Case 2.  u - 3 = 0\r\n" );
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document.write( "                 u = 3\r\n" );
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document.write( "                \"sqrt%28e%5Ex%29\" = 3\r\n" );
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document.write( "                \"e%5Ex\" = 9\r\n" );
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document.write( "                x = \"ln%289%29%29\" = 2*ln(3).  \r\n" );
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document.write( "                It is the answer for Case 2.\r\n" );
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document.write( "ANSWER.  The given equation has two solutions,  -2*ln(2)  and  2*ln(3).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "The solution by @greenestamps has editorial deficiencies, \r
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\n" ); document.write( "\n" ); document.write( "so I came to fix them.\r
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