# Maximum Possible Ratio With Digit Counting Function

Calculus Level 3

Let $$d(n)$$ denote the number of digits of $$n$$. For example, $$d(1929) = 4$$ and $$d(301) = 3$$.

What is the maximum value of the ratio $\dfrac{\big(d(n)\big)^6}{n}$ as $$n$$ ranges over the positive integers?

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