Can someone explain this, please?

Test Preparation SAT Subject Test Preparation
1

<p>If log_b(xy) < 0, which of the following must be true?</p>

<p>A. xy < 0
B. xy < 1
C. xy > 1
D. xy > 0
E. none of the above.</p>

<p>Answer Explanation:
E. If b < 1, Choice B is the correct answer. If b < 1, Choice C is the correct answer. Since no restriction was put on B, however, the correct answer is Choice E.</p>

<p>What I don't understand is why the answer is E rather than D. Log_b(N) is only defined for positive N, so wouldn't the answer be D, since xy must be positive? Or maybe I'm just not seeing something that's really obvious... Thanks :D</p>

2

<p>Assuming b is positive, I believe D would be correct.</p>

<p>If b is negative, you’d be dealing with complex numbers, which you cannot say that they’re “less than zero.”</p>

3

<p>Okay, I get it now. Thanks. I assumed we were only dealing with the reals…</p>

4

<p>Yeah, no problem…if b > 0, D must be true. If any of the other choices (A,B,C) must be true, the problem’s screwed up.</p>