How many digits do I really have?

Determine the number of digits of \(10,000,000! \).

Details and Assumptions

It is 10 million factorial.

You may use the following approximation:
\( \log_{10} 2 = 0.30102999566398 \ldots \)
\( \log_{10} \pi = 0.49714987269413 \ldots \)
\( \log_{10} e = 0.43429448190325 \ldots \)

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