If p > 1 and q = 2^(p −1), then 4^p =
If p > 1 and q = 2^(p −1), then 4^p =
Answer/Solution
4q^2
Steps/Work
If p > 1 and q = 2^(p −1), then 4^p
Given p>1, so let's assume p=2
q=2^(p-1) = 2^(2-1) = 2, so q=2
hence, 4^p = 4^2 = 16
only 1 ans. choice can satisfy this:
A) 16q^2 --> clearly > 16
B) 4q^2 --> 4*2^2 = 16(we can stop after this as there can be only 1 right answer)
C) q^2 --> clearly < 16
D) q^2/4 --> clearly < 16
E) q^2/16 --> clearly < 16
Ans. B) 4q^2
Given p>1, so let's assume p=2
q=2^(p-1) = 2^(2-1) = 2, so q=2
hence, 4^p = 4^2 = 16
only 1 ans. choice can satisfy this:
A) 16q^2 --> clearly > 16
B) 4q^2 --> 4*2^2 = 16(we can stop after this as there can be only 1 right answer)
C) q^2 --> clearly < 16
D) q^2/4 --> clearly < 16
E) q^2/16 --> clearly < 16
Ans. B) 4q^2