2020 AIME I Problem 2

There is a unique positive real number x such that the three numbers \log_8(2x),\log_4x, and \log_2x, in that order, form a geometric progression with positive common ratio. The number x can be written as \tfrac{m}{n}, where m and n are relatively prime positive integers. Find m+n.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.