If a,b &gt;0 and c&gt; a+b, then prove that lga + lgb &...

Question

If a,b >0 and c> a+b, then prove that lga + lgb < 2*lgc -2.

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lga+lgb ≤2*lgc -2 is equivalent with: lg(ab) ≤2*lgc -2 (according to property 1)
Moving further one step, this is equivalent to prove that:
2*lgc -lg(ab) ≥2 which is the same with lg(c^2) -lg(ab) ≥2 (property 3)...

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