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If log2(1+1/a)+log2(1+1/b)+log2(1+1/c)=...

If `log_2(1+1/a)+log_2(1+1/b)+log_2(1+1/c)=2` where `a,b,c` are three different positive integers, then that `log_e(a+b+c)=log_e a+log_eb+log_ec` or prove that `a=1,b=2,c=3.`

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