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Question Number 111374 by mathdave last updated on 03/Sep/20

Commented by kaivan.ahmadi last updated on 03/Sep/20

$$={log}_{\sqrt{3}}(\sqrt{14}-\sqrt{5})+{log}_{\sqrt{3}}(\sqrt{14}+\sqrt{5})=$$$${log}_{\sqrt{3}}(\sqrt{14}-\sqrt{5})(\sqrt{14}+\sqrt{5})={log}_{\sqrt{3}}(14-5)=$$$${log}_{\sqrt{3}}9={log}_{3^{\frac{1}{2}}}{3}^2=2\times 2{log}_{3}3=4$$

Answered by mnjuly1970 last updated on 03/Sep/20

$$ans:4$$

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