If \(N = 2^{0.15}\) and \(N^b = 16,\) \(b\) must equal.

[M7MBA]

If \(N = 2^{0.15}\) and \(N^b = 16,\) \(b\) must equal.

A. \(\dfrac3{80}\)
B. \(\dfrac35\)
C. \(4\)
D. \(\dfrac53\)
E. \(\dfrac{80}3\)

Answer: E

Source: Magoosh

[Scott@TargetTestPrep]

If \(N = 2^{0.15}\) and \(N^b = 16,\) \(b\) must equal.

A. \(\dfrac3{80}\)
B. \(\dfrac35\)
C. \(4\)
D. \(\dfrac53\)
E. \(\dfrac{80}3\)

Answer: E

Solution:

Substituting 2^0.15 for N in the second equation, we have:

(2^0.15)^b = 16

2^(0.15b) = 2^4

0.15b = 4

b = 4/0.15 = 400/15 = 80/3

Answer: E