我觉得要解释您的问题,还是要先准确理解翻译和相关数学知识。An important property of base-10 logarithms, which makes them so useful in calculations, is that the logarithm of numbers greater than 1 that differ by a factor of a power of 10 all have the same fractional part.我认为的意译:以10为底的对数有一个重要性质,即仅有小数点位置不同的正数的对数尾数(尾数即小数部分)相同,这一点使其在计算中非常有用。举例:lg 0.5、lg 5、lg 50的对数尾数均相同。再来回答您的问题。问题1:分析结构: the logarithm of (numbers (greater than 1 其实是numbers that greater than one 的省略)) (that differ by a factor of a power of 10 all have the same fractional part 这个定语从句才是修饰logarithm的,不可能前后两个定从都修饰logarithm)。问题2:that differ by a factor of a power of 10 all have the same fractional part.是定语从句吗?回答同上,是修饰logarithm的定语从句。by应该怎么翻译?differ是差别,by是连接差异所在的介词。differ by可以看作数学里常用的搭配,就是差别/相差,比如 There are two numbers, differ by 10. 这两个数相差10。