Math Challenge!?

Question

1.How many numbers between 100 and 200 can be expressed as powers of 2?Show steps.
2.Which power of 2 is closest to 1000?

Answer 1

#1: Just one - 128=2^7. 2^8=256 is too high, and 2^6=64 is too low.
#2: 2^10 = 1024

Answer 2

There can be only one number that is a power of 2 between 100 and 200.

Reasoning: Since 200 = 100 x 2, and adding one to the power on 2 is the same as multiplying by two, there can be only one number between the two that is a power of 2.

The power of 2 that is closest to 1000 is 1012 or 2^10

Answer 3

Well, grab a number and try it out:

2^5 = 32 Not high enough
2^6 = 64 Nope
2^7 = 128 There's one.
2^8 = 256 That's over 200, so there's only one between 100 and 200.

Let's keep going to find the one closest to 1000
2^9 = 512
2^10 = 1024 This looks good!

Answer 4

2^n > 100
nln(2) > ln(100)
n> ln(100)/ln(2)
n>6.64
2^n < 200 => n < ln(200)/ln(2) (by the same method) so
n < 7.64
and the only integer in the range
6.64 < n < 7.64 is n = 7.
So there's only one exact power of 2 between 100 and 200 and it's
2^7 = 128

2^9 = 512 and 2^10 = 1024 so I'd say it's 2^10 (unless the question meant 'closest to but not exceeding')

HTH

Doug

Answer 5

2^7 = 128 is the only one
because the next lower and next higher power are clearly out of the range

2^10 = 1024 is the closest,
again try the next higher and lower and you'll see

Answer 6

1. 2^7=128
2^8=256

1 number

2. 1024

Answer 7

1)
1,2,4,8,16,32,64,128,256
so, 1 of them :128

2)1024, or 2^ 10

Answer 8

sry but that question is hard n i personally think math sux.good luck tho :)