101 to the 101

Algebra Level 3

Given that 2.004<log10101<2.005 2.004 < \log_{10} 101 < 2.005, how many digits are there in the decimal representation of 101101 101^{101}?

Details and assumptions

Clarification: The decimal representation of 2102^{10} is 210=10242^{10}=1024, which has 4 digits.

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