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I need to figure out this log function

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I'm making an RPG
The aim here to to make the time between "re-occurrences" (the element shows up) shrink with every passing day until it gets infinitely close to 4 but..


it never reaches it. I know this function has something to do with log but I just can't figure out the formula for this curve

(BTW the value during day 1 is 8)

please help me.


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