SOLUTION: Hi, Can you please help, . Solve {{{ e^x + e^(-x) = 5 }}}, for "x" . Thanks ahead of time, Levi

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Hi, Can you please help, . Solve {{{ e^x + e^(-x) = 5 }}}, for "x" . Thanks ahead of time, Levi      Log On


   

Question 168632: Hi, Can you please help,
.
Solve +e%5Ex+%2B+e%5E%28-x%29+=+5+, for "x"
.
Thanks ahead of time, Levi
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve +e%5Ex+%2B+e%5E%28-x%29+=+5+, for "x"
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cosh%28x%29+=+%28e%5Ex+%2B+e%5E%28-x%29%29%2F2
x = arc+cosh%282.5%29
x = 1.5668 (via calculator)
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This is not a rigorous solution. I'll work on it more tomorrow.
If you post it again, perhaps someone else can solve it.
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OK, I figured it out.
+e%5Ex+%2B+e%5E%28-x%29+=+5+
+e%5E2x+%2B+1+=++5e%5E%28x%29+
+e%5E2x+-+5e%5E%28x%29%2B+1+=+0 (a quadratic in e^x)
e^x = (5 + sqrt (21))/2
e^x = (5 - sqrt (21))/2
x = ln(above)