计算 (lg1/2+lg1+lg2+lg4+lg8+.+lg1024)*log2 10
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![计算 (lg1/2+lg1+lg2+lg4+lg8+.+lg1024)*log2 10](/uploads/image/z/2643042-66-2.jpg?t=%E8%AE%A1%E7%AE%97+%28lg1%2F2%2Blg1%2Blg2%2Blg4%2Blg8%2B.%2Blg1024%29%2Alog2+10)
计算 (lg1/2+lg1+lg2+lg4+lg8+.+lg1024)*log2 10
计算 (lg1/2+lg1+lg2+lg4+lg8+.+lg1024)*log2 10
计算 (lg1/2+lg1+lg2+lg4+lg8+.+lg1024)*log2 10
原式=lg(1/2*1*2*4*……*1024)*log2(10)
=lg[2^(-1+0+1+2+3+4+5+6+7+8+9+10)]*(lg10/lg2)
=lg(2^54)*(1/lg2)
=54lg2/lg2
=54