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If r and s are positive integers such that (2^r)(4^s) = 16,
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10 Jul 2020, 08:02
10 Jul 2020, 08:02
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Question Stats:
58% (00:58) correct
41% (01:33) wrong based on 31 sessions
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If r and s are positive integers such that \((2^r)(4^s) = 16\), then \(2r + s = \)
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Re: If r and s are positive integers such that (2^r)(4^s) = 16,
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11 Jul 2020, 08:40
11 Jul 2020, 08:40
1
We are given that r and s are non-zero, positive integers (ex. 1, 2, 3, etc.)
Since we are raising 2 and 4 to the power of a non zero integer, the resultant will be equal or larger than the original base (2 or 4)
Now lets consider what each of our numbers could equal:
(2^r) can take several values dependent on what r is. It can be 2 (if r=1), 4 (r=2), 8 (r=3), and 16 (r=4)
(4^s) can equal to 4 (if s=1), and 16 (if s=2)
s cannot equal 2, because then we will have (2^r) *16 = 16, this would mean that 2^r equals to 1 which indicates that r=0 (violates the clause that r is a positive integer)
Thus s can only equal to 1 and 4^s must only equal to 4.
Then 2^r must equal to 4. Which is only possible if r=2
Now we just compute 2r+s= (2)(2) + 1(1) = 5 (Answer D)
Since we are raising 2 and 4 to the power of a non zero integer, the resultant will be equal or larger than the original base (2 or 4)
Now lets consider what each of our numbers could equal:
(2^r) can take several values dependent on what r is. It can be 2 (if r=1), 4 (r=2), 8 (r=3), and 16 (r=4)
(4^s) can equal to 4 (if s=1), and 16 (if s=2)
s cannot equal 2, because then we will have (2^r) *16 = 16, this would mean that 2^r equals to 1 which indicates that r=0 (violates the clause that r is a positive integer)
Thus s can only equal to 1 and 4^s must only equal to 4.
Then 2^r must equal to 4. Which is only possible if r=2
Now we just compute 2r+s= (2)(2) + 1(1) = 5 (Answer D)
Re: If r and s are positive integers such that (2^r)(4^s) = 16,
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11 Jul 2020, 10:15
11 Jul 2020, 10:15
1
Step 1: Understanding the question:
r and s are positive integers
2^r *4^s = 16
2^r*2^2s = 2^4
2^(r+2s)= 2^4
r+2s = 4
When r=2, s=1 only possibility
Step 2: Calculation
2r+s = 4+1 = 5
(D) is correct
My channel URL: https://www.youtube.com/channel/UCvdY0k ... EOsT5PMFRQ
r and s are positive integers
2^r *4^s = 16
2^r*2^2s = 2^4
2^(r+2s)= 2^4
r+2s = 4
When r=2, s=1 only possibility
Step 2: Calculation
2r+s = 4+1 = 5
(D) is correct
My channel URL: https://www.youtube.com/channel/UCvdY0k ... EOsT5PMFRQ
