(a) Without using Mathematical tables, find x, given that (6 log (x + 4) = log 64)
(b) If (U = {1, 2, 3,4, 5, 6, 7, 8, 9, 10}, X = {1, 2, 4, 6, 7, 8, 9}, Y = {1, 2, 3, 4, 7, 9}) and (Z = {2, 3, 4, 7, 9}). What is (X cap Y cap Z’ )?
Explanation
(a) (6 log (x + 4) = log 64)
(implies (x + 4)^{6} = 64)
((x + 4)^{6} = 2^{6})
(implies x + 4 = 2 ; x = 2 – 4 = -2)
(therefore x = -2)
(b) (U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10})
(X = {1, 2, 4, 6, 7, 8, 9}; Y = {1, 2, 3, 4, 7, 9} ; Z = {2, 3, 4, 7,9})
(X cap Y = {1, 2, 4, 7, 9})
({1, 2, 4, 7, 9} cap Z’ = {1, 2, 4, 7, 9} cap {1, 5, 6, 8, 10})
= {1}