For integers a and b, 16a = 32^b. Which of the following correctly expresses a in terms of b?

[BTGmoderatorDC]

For integers a and b, 16a = 32^b. Which of the following correctly expresses a in terms of b?

A. a = 2^b
B. a = 4^b
C. a = 2^(5b − 4)
D. a = 4^(5b − 4)
E. a = 2^(5b)


OA C

Source: Veritas Prep

[Ian Stewart]

16a = 32^b
(2^4)a = (2^5)^b
(2^4)a = 2^(5b)
a = 2^(5b) / 2^4
a = 2^(5b - 4)