Theory question 101
Logarithms(a) Without using Mathematics Tables, find x, given that 6log (x + 4) = log 64 (b) if U = (1,2,3,4,5,6,7,8,9,10) X = (1,2,4,5,7,8,9) Y = (1,2,3,4,7,9) and Z = (2,3,4,7,9), what is X∩Y∩Z?
Show the model answer
Model answer
(a) 6 log(x + 4) = log (x + 4)6 and log 64 = log 26.
So (x + 4)6 = 26 ⇒ x + 4 = 2 ⇒ x = −2 (x + 4 must be positive for the log to exist).
(b) X∩Y = {1, 2, 4, 7, 9}
X∩Y∩Z = {2, 4, 7, 9}
(If the question means Z′ = {1, 5, 6, 8, 10}, then X∩Y∩Z′ = {1}.)
Explanation
Write 64 as a power of 2 so both sides have the same power.