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Under what conditions is the following inequality true for $a, b>0$
$$
\log _e(a+b) \geq \lambda \log _e(a / \lambda)+(1-\lambda) \log _e(b /(1-\lambda))
$$

  1. $\lambda=0.5$
  2. $0<a / \lambda \leq 1, b /(1-\lambda)>0$
  3. $a / \lambda>0,0<b /(1-\lambda) \leq 1$
  4. All of the above
  5. None of the above
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