document.write( "Question 270973: e x+ e -x=5 \n" ); document.write( "

Algebra.Com's Answer #198483 by Alan3354(69443) $\"\"$ $\"About$

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If you mean
\n" ); document.write( "e^x + e^-x = 5 then
\n" ); document.write( "x = inv hyperbolic cosine (2.5)
\n" ); document.write( "x =~ 1.566799 (via calculator)
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\n" ); document.write( "The long way
\n" ); document.write( "e^x + e^-x = 5
\n" ); document.write( "Multiply by e^x
\n" ); document.write( "e^2x + 1 = 5e^x
\n" ); document.write( "e^2x - 5e^x + 1 = 0
\n" ); document.write( "It's a quadratic in e^x
\n" ); document.write( "e^x = (1/2)*(5 ą sqrt(21))
\n" ); document.write( "e^x =~ 4.7912878, 0.2087
\n" ); document.write( "x = log(4.79..., 0.2087)
\n" ); document.write( "x = ą 1.566799
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