ASMO Math 2022 — Grade 10 — School Round Question 17

Compute $\frac{1}{\log_2(2\sqrt{3})}+\frac{1}{\log_8(2\sqrt{3})}+\frac{1}{\log_3(2\sqrt{3})}+\frac{1}{\log_3(2\sqrt{3})}$.