101 to the 101

Algebra Level 3

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

Details and assumptions

Clarification: The decimal representation of \(2^{10}\) is \(2^{10}=1024\), which has 4 digits.

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