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

[Gmat_mission]

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. \(a = 2^{5b}\)

[spoiler]OA=C[/spoiler]

Source: Veritas Prep

[Scott@TargetTestPrep]

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. \(a = 2^{5b}\)

[spoiler]OA=C[/spoiler]

Source: Veritas Prep

Solution:

16a = 32^b

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

Answer: C