Happy log day

Algebra Level 3

ln(a+b3)=ln(a)+ln(b)2,ab+ba= ? \large \ln\left(\dfrac {a+b}3\right) = \dfrac{\ln(a) + \ln(b)}2 \qquad , \qquad \dfrac ab + \dfrac ba = \ ?

Take a,b>0a,b> 0.

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