So I have been using Minesweeper Online as a way to practice my Minesweeper skills. I recently found the settings, which has an Advanced Settings section where I am able to look at more statistics from my games, and one of them is IOS (Index Of Speed), which is defined as$$IOS:=\dfrac{\log(\text{3BV})}{\log(t+1)}$$(in the settings, the denominator is shown as $t-1$, however I am completely sure that this is a typo as then board completions of 1 second or under would render the IOS as a complex number, which is impossible.)
where $t$ is how much time has elapsed and 3BV is the minimum number of clicks needed to complete a board.
My question is: How is this formula derived? I sort of know what's going on because it's a ratio of minimum clicks to time, but what I am confused about is how logarithms factor into this.