$$
\begin{aligned}
f(a,b,\lambda) & =\lambda^{-1}\log(e^{\lambda a}+e^{\lambda b}) \\
& \leq\lambda^{-1}\log\left(2e^{\lambda\max(a,b)}\right) \\
& =\lambda^{-1}(\log2+\lambda\max(a,b)) \\
& =\max(a,b)+\frac{\log2}{\lambda}
\end{aligned}
$$
2倍在指数前而不是后面
