# exponential equation

sage: solve(exp(-x)+exp(x) == 2,x)
[x == 0]
sage: solve(exp(-2*x)+exp(2*x) == 2,x)
[]

Can tell me anyone why the second equation has no solution?

exponential equation

sage: solve(exp(-x)+exp(x) == 2,x)
[x == 0]
sage: solve(exp(-2*x)+exp(2*x) == 2,x)
[]

Can tell me anyone why the second equation has no solution?

1

I unfortunately don't have time to check why this doesn't work, but the following keyword argument (useful to know in any case) does work:

```
sage: (exp(-2*x)+exp(2*x) == 2).solve(x,to_poly_solve=True)
[x == I*pi*z15]
```

which should be interpreted as saying `z15`

is a free integer variable (hence `z`

). One can also do

```
sage: (exp(-x)+exp(x) == 2).solve(x,to_poly_solve='force')
[x == 2*I*pi*z24]
```

for all possible solutions to the original one. Unfortunately, finding the documentation for this (currently) requires using the method notation instead of functional

```
sage: solve?
```

notation.

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Asked: ** 2010-10-02 13:35:11 +0200 **

Seen: **2,902 times**

Last updated: **Oct 02 '10**

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For the record, this question is closely related to http://ask.sagemath.org/question/156/exponential-equation-real-solution