# Sums|smuS

The sum of the base-$$10$$ logarithms of the factors of $$10^n$$ is 792 ($$\log n_1+\log n_2+...\log n_k$$) where $$n_k$$ are the factors of $$10^n$$. What is $$n$$?

EDIT: The problem has been updated to $$10^n$$ instead of $$10n$$.

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