Theory question 106
Logarithms(a) Using mathematical tables, find; (i) 2 sin 63.35° (ii) log cos 44.74°
(b) Find the value of K given that log K − log (K − 2) = log 5.
(c) Use logarithm tables to evaluate (3.68)2 × 6.705/√0.3581
Show the model answer
Model answer
(a)(i) sin 63.35° = 0.8938, so 2 sin 63.35° = 1.7876
(ii) cos 44.74° = 0.7103, log 0.7103 = 1̄.8514
(b) log(K/(K − 2)) = log 5, so K = 5(K − 2), 4K = 10, K = 2.5
(c) log 3.68 = 0.5658; × 2 = 1.1316; + log 6.705 (0.8264) = 1.9580
log 0.3581 = 1̄.5540; ÷ 2 for the root = 1̄.7770
1.9580 − 1̄.7770 = 2.1810; antilog ≈ 151.7
Explanation
To take a square root with logs, halve the log (handle the negative characteristic carefully).