Theory question 104
Indices and LogarithmsSolve: 2(2y+2) − 9(2y) = −2
Show the model answer
Model answer
22y+2 = 4(2y)2; let p = 2y
4p2 − 9p + 2 = 0
(4p − 1)(p − 2) = 0, p = ¼ or p = 2
2y = 2 gives y = 1; 2y = ¼ = 2−2 gives y = −2
y = 1 or y = −2
Explanation
Substitute p = 2^y to get a quadratic.