How to get from counting nines to the formula n*(9/10)^log_10(n)

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quddusaliquddus
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Hi.
How would I go from seeing the pattern in the number of nines in the first n numbers, to writing the following formulae for it:

n*(9/10)^log_10(n)

I don't get how to put the log in (or how it works). Sorry, it is an easy question. Please help.
 
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One method would be to draw a graph of the number of 9s vs the number n, then fit a curve to it. This would, I think, require a computer since this is obviously not an intuitive relationship.
 
I want to delete this thread: Don't know how to!
 
I don't need the answer...pls dnt ask y - loong story i'd rather not say.

I apologise for wasting your time.