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Given that 2.004<log10101<2.005 2.004 < \log_{10} 101 < 2.0052.004<log10101<2.005, how many digits are there in the decimal representation of 101101 101^{101}101101?
Details and assumptions
Clarification: The decimal representation of 2102^{10}210 is 210=10242^{10}=1024210=1024, which has 4 digits.
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