Determining constant values from 3 equations I have the following three equations:
$$\begin{align*}
k_1 + k_3 &= 0\\
k_1e^{k_2(0.1)} + k_3 &= 1\\
k_1e^{k_2(1)} + k_3 &= 100
\end{align*}$$
How do you go about solving for values $k_1$, $k_2$, and $k_3$?
Obviously $k_1$, $k_3$ are related in the fact one must be the negative of the other to make the first equation true. All that is given in lecture is "Mathematica determines the constants of these three equations to be...", it doesn't actually explain how to solve them yourself.
Thanks.

$k_3=-k_1$. 
$k_1e^{(1/10)k_2}-k_1=1$ yields $k_1={1\over e^{(1/10)k_2}-1}$ 
$k_1e^{k_2}-k_1=100$ yields $k_1={100\over e^{k_2}-1}$ 
So we have $${1\over e^{(1/10)k_2}-1}={100\over e^{k_2}-1}$$ to solve for $k_2$. 
$e^{k_2}-1=100(e^{(1/10)k_2}-1)$ 
Let $Q=e^{(1/10)k_2}$. Then $Q^{10}-1=100Q-100$, $Q^{10}-100Q+99=0$. 
One solution of this equation is $Q=1$, which leads to $k_2=0$, which we must reject --- it slipped in when we divided by $e^{k_2}-1$. 
That leaves a polynomial of degree $9$. There is in general no closed form formula for the solution of such an equation. Mathematica uses numerical methods, for example, the calculus-based Newton's Method. 
