ASMO Math 2022 — Grade 11 — School Round Question 11

Evaluate $\frac{1}{\log_2(4\sqrt{5})}+\frac{1}{\log_5(4\sqrt{5})}+\frac{1}{\log_4(4\sqrt{5})}+\frac{1}{\log_2(4\sqrt{5})}$.