Problem: Of the following
(1) a(x−y)=ax−ay
(2) ax−y=ax−ay
(3) log(x−y)=logx−logy
(4) logylogx=logx−logy
(5) a(xy)=ax⋅ay
Answer Choices:
A. only 1 and 4 are true
B. only 1 and 5 are true
C. only 1 and 3 are true
D. only 1 and 2 are true
E. only 1 is true
Solution:
Of the four distributive laws given in statements (1), (2), (3) and (5), only (1) holds in the real number field. Statement (4) is not to be confused with log(x/y)=logx−logy.∴(E) is the correct choice.