Gabriel's digits

How many digits are there in the decimal expansion of 620 6^{20} ?

This problem is posed by Gabriel M.

Details and assumptions

You may use the fact that 0.30<log102<0.31 0.30 < \log_{10} 2 < 0.31 and 0.47<log103<0.48 0.47 < \log_{10} 3 < 0.48 .

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