Find n satisfying the equation [\log_21]+[\log_22]+[\log_23]+…[\log_2n]=1538

Laney Spears

Laney Spears

Answered question

2022-01-22

Find n satisfying the equation [log21]+[log22]+[log23]+[log2n]=1538

Answer & Explanation

Ydaxq

Ydaxq

Beginner2022-01-23Added 12 answers

For all j such that 2kj<2k+1 for some integer k, we have
[logj]=k. Further note that there are exactly 2k js that [log[j]=k holds. Hence from holds. Hence from
0+1×2+2×22+3×23+4×24+5×25+6×26+7×27=1538
, we can easily obtain
([log21])+([log22]+[log23])++([log2(27)++log2(281)])=1538
utgyrnr0

utgyrnr0

Beginner2022-01-24Added 11 answers

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