Theory question 102
Logarithms(a) Given that log102 = 0.3010, log107 = 0.8451 and log105 = 0.6990, evaluate without using logarithm tables. (i) log1035; (ii) log102.8
(b) Given that N0.8942 = 2.8, use your result in (a)(ii) to find the value of N.
Show the model answer
Model answer
(a)(i) log 35 = log 7 + log 5 = 0.8451 + 0.6990 = 1.5441.
(ii) log 2.8 = log (7 × 4/10) = log 7 + 2 log 2 − log 10 = 0.8451 + 0.6020 − 1 = 0.4471.
(b) 0.8942 log N = log 2.8 = 0.4471, so log N = 0.5.
N = 100.5 = √10 ≈ 3.162.
Explanation
Break each number into factors whose logs you are given.