※ 引述《shingai (shingai)》之銘言：
: 題為
: 8^100 =(a_n)*3^n+(a_(n-1))*3^(n-1)+...+(a_1)*3+(a_0)
: , 其中 a_i in {0,1} , i in {1,2,...,n}
: 當a_n=1時, 試求 n值
: _______________________________________________________
3^n < 8^100 < 3^n+3^(n-1)+3^(n-2)+...+3^1+1 = [3^(n+1)-1]/2
=> n < log (8^100) < log [3^(n+1)-1]/2 < log 3^(n+1)/2 = n+1-log 2
3 3 3 3
=> n < 100*(log8/log3) < n+1-(log2/log3)
=> n < 189.2789... < n+1-0.6309 = n+0.3691
∴ n=189
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