Theory question 101
Logarithms(a) Evaluate without using the mathematical table or calculator. log10√30 − log10√6 + log10√2.
(b) U = {1, 2, 3, ........... 10}, A = {1, 2, 3, 4, 5}, B = {2, 3, 5} and C = {6, 8, 10}. (i) Given that the Venn diagram represents the sets above, copy and fill in the elements. (ii) Find A∩C. (iii) Find A∩B'.
Show the model answer
Model answer
(a) log √(30 × 2/6) = log √10 = ½ log 10 = ½.
(b)(i) B inside A: put 2, 3, 5 in B; 1 and 4 in A outside B; 6, 8, 10 in C (separate from A); 7 and 9 outside all sets.
(ii) A∩C = ∅ (no common elements).
(iii) A∩B' = {1, 4}.
Explanation
Combine the logs first, then use log √10 = ½.