Theory question 109
Indices and Logarithms(a) Without using mathematical tables or calculator, evaluate ((3/2)log 27 − 3 log 5√5)/log 0.6.
(b) Two linear transformations A and B in the Oxy plane, are defined by A: (x, y) → (x + 2y, −x + y), B: (x, y) → (2x + 3y, x + 2y). (i) Write down the matrices A and B. (ii) Find the image of the point P(−2, 2) under the linear transformation A followed by B.
Show the model answer
Model answer
(a) (3/2)log 27 = (9/2)log 3 and 3 log 5√5 = (9/2)log 5. Numerator = (9/2)log(3/5) = (9/2)log 0.6, so the value is 9/2.
(b)(i) A = (1 2 / −1 1), B = (2 3 / 1 2) (rows separated by /).
(ii) A(−2, 2) = (2, 4); then B(2, 4) = (16, 10).
Explanation
Write 27 and 5√5 as powers of 3 and 5.