NECO 2004 Mathematics · Question 28

Evaluate (Log13 - log5) ÷ X(log5-log13) without using tables

Options

A.X
B.–x
C.X-1
D.–X-1
E.-1

Answer: D. –X-1

Explanation written with AI and checked against the answer key

The expression is (log 13 − log 5) ÷ X(log 5 − log 13), and the question says "without using tables". Step 1: Spot the relationship Let a = log 13 − log 5. Then log 5 − log 13 = −a. Step 2: Substitute (log 13 − log 5) ÷ [X(log 5 − log 13)] = a ÷ [X(−a)] = −1/X = −X⁻¹ Step 3: Match the option −1/X is the same as −X⁻¹, which is option D. Check: Option D, "–X-1", is read as −X⁻¹, which equals −1/X. This matches our working. Option E (−1) would only be correct if there were no X in the denominator, and option B (−x) is not equal to −1/X. Tip: When you see the same terms in a different order, such as (a − b) and (b − a), remember that (b − a) = −(a − b). The two brackets cancel and leave a −1. Here the leftover X stays in the denominator and gives −1/X.

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