Theory question 106
Logarithms(a)(i) Given that log105 = 0.699 and log103 = 0.477, find log1045, without using mathematical tables.
(ii) Hence, solve x0.8265 = 45
(b) Use mathematical tables to evaluate √(2.067/(0.0348 × 0.538))
Show the model answer
Model answer
(a)(i) log 45 = log(9 × 5) = 2 log 3 + log 5 = 0.954 + 0.699 = 1.653
(ii) Take logs: 0.8265 log x = log 45 = 1.653
log x = 1.653 ÷ 0.8265 = 2, so x = 102 = 100
(b) log 2.067 = 0.3154; log 0.0348 = 2̄.5416; log 0.538 = 1̄.7308
Denominator: 2̄.5416 + 1̄.7308 = 2̄.2724
0.3154 − 2̄.2724 = 2.0430; ÷ 2 = 1.0215
antilog 1.0215 ≈ 10.51
Explanation
log 45 = log 9 + log 5, and log 9 = 2 log 3.