Under what conditions is the following inequality true for $a, b>0$
$$
\log _e(a+b) \geq \lambda \log _e(a / \lambda)+(1-\lambda) \log _e(b /(1-\lambda))
$$
- $\lambda=0.5$
- $0<a / \lambda \leq 1, b /(1-\lambda)>0$
- $a / \lambda>0,0<b /(1-\lambda) \leq 1$
- All of the above
- None of the above