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Algebra Level 3

Find the positive integer nn, for which log21+log22+log23++log2n=1994.\lfloor \log_2{1}\rfloor+\lfloor\log_2{2}\rfloor+\lfloor\log_2{3}\rfloor+\cdots+\lfloor\log_2{n}\rfloor=1994.

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