document.write( "Question 168634: Hi, Can you please help,
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\n" ); document.write( "Solve \"+e%5Ex+%2B+e%5E%28-x%29+=+5+\", for \"x\"
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\n" ); document.write( "I would like some answers quickly, so I can put it down for notes for a quiz tommorrow.
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\n" ); document.write( "Thanks ahead of time, Levi \n" ); document.write( "
Algebra.Com's Answer #124272 by stanbon(75887)\"\" \"About 
You can put this solution on YOUR website!
e^x + e^(-x) = 5\r
\n" ); document.write( "\n" ); document.write( "e^x + 1/e^x = 5
\n" ); document.write( "Multiply thru by e^x to get:\r
\n" ); document.write( "\n" ); document.write( "e^2x + 1 = 5 e^x
\n" ); document.write( "Rearrange to form a quadratic equation:\r
\n" ); document.write( "\n" ); document.write( "(e^x)2 - 5e^x + 1 = 0
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\n" ); document.write( "Change the variable: Let w = e^x
\n" ); document.write( "Rewrite:
\n" ); document.write( "w^2 - 5w + 1 = 0
\n" ); document.write( "Use the quadratic formula:
\n" ); document.write( "w = [5 +- sqrt(25-4*1)]/2
\n" ); document.write( "w = [5 +- sqrt(21)]/2
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\n" ); document.write( "Change back to e^x
\n" ); document.write( "e^x = [5 + sqrt(21)]/2 or e^x = [5 - sqrt(21)]/2
\n" ); document.write( "Take the natural log of both sides to get:
\n" ); document.write( "x = ln[[5 + sqrt(21)]/2] or x = ln[[5 - sqrt(21)]/2]
\n" ); document.write( "x = ln[4.79129] or x = ln[208712]
\n" ); document.write( "x = 1.5668 or x = -1.5668
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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