Let $x \mapsto e^x$ be the D1932: Standard natural real exponential function.
Let $a, b, t \in \mathbb{R}$ each be a D993: Real number such that

(i)	\begin{equation} b < b \end{equation}
(ii)	\begin{equation} u : = \lambda (b - a) \end{equation}
(iii)	\begin{equation} \lambda : = - \frac{a}{b - a} \end{equation}
(iv)	\begin{equation} g(u) : = - \lambda u + \log(1 - \lambda + \lambda e^u) \end{equation}

Then \begin{equation} e^{g(u)} = - \frac{a}{b - a} e^{b t} + \frac{b}{b - a} e^{t a} \end{equation}