Theory question 101
LogarithmsGiven that log102 = 0.3010 and log103 = 0.4771, calculate without using mathematical tables or calculator, the value of: (a) log1054, (b) log100.24.
Show the model answer
Model answer
(a) 54 = 2 × 33: log 54 = log 2 + 3 log 3 = 0.3010 + 1.4313 = 1.7323.
(b) 0.24 = 23 × 3 ÷ 100: log 0.24 = 3(0.3010) + 0.4771 − 2 = 1.3801 − 2 = −0.6199 (= 1̄.3801).
Explanation
Write each number as a product of powers of 2, 3 and 10.