WAEC 2014 Mathematics · Question 42
If log 5.957 = 0.7750, find log
Options
- A..1986
- B..9250
- C..5917
- D..075
Answer: B. .9250
Explanation written with AI and checked against the answer key
The expression "3 √0.0005957" is ambiguous. It most likely means the cube root of 0.0005957, i.e. ∛0.0005957. I'll work through that and also check the other reading. Step 1: Write 0.0005957 in standard form 0.0005957 = 5.957 × 10⁻⁴ Step 2: Take the log log(0.0005957) = log 5.957 + log 10⁻⁴ = 0.7750 − 4 = 4̄.7750 Step 3: Cube root means divide the log by 3 log ∛(0.0005957) = (−4 + 0.7750) ÷ 3 = −3.2250 ÷ 3 = −1.0750 Step 4: Write in bar form −1.0750 = −2 + 0.9250 = 2̄.9250 Check the alternative reading: if it meant 3 × √0.0005957, then log = log 3 + ½(−3.225) = 0.4771 − 1.6125 = −1.1354 = 2̄.8646, which matches no option. So the cube root interpretation is the intended one. Answer: B (2̄.9250) Tip: When taking a root of a log with a negative characteristic, add enough to the characteristic to make it divisible by the root. Here, 4̄.7750 = −6 + 2.7750, so dividing by 3 gives −2 + 0.9250 = 2̄.9250. Always convert to a negative integer plus a positive decimal before dividing.AI can make mistakes. Report anything that looks wrong.
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