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For integers x and y, 3^(4x+12)=5^(3x+y). What is the value of y? A.
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01 Jul 2022, 05:57
01 Jul 2022, 05:57
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For integers \(x\) and \(y\), \(3^{(4x+12)}=5^{(3x+y)}\). What is the value of y?
A. -12
B. -3
C. 0
D. 9
E. Cannot be determined
A. -12
B. -3
C. 0
D. 9
E. Cannot be determined
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
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GRE Math Essentials (2022)
GRE Geometry Formulas for a Q170
GRE - Math Book
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GRE Math Essentials (2022)
GRE Geometry Formulas for a Q170
GRE - Math Book
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Re: For integers x and y, 3^(4x+12)=5^(3x+y). What is the value of y? A.
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01 Jul 2022, 06:19
01 Jul 2022, 06:19
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Carcass wrote:
For integers \(x\) and \(y\), \(3^{(4x+12)}=5^{(3x+y)}\). What is the value of y?
A. -12
B. -3
C. 0
D. 9
E. Cannot be determined
A. -12
B. -3
C. 0
D. 9
E. Cannot be determined
If \(x\) and \(y\) are integers, the only way \(3^{(4x+12)}\) can equal \(5^{(3x+y)}\) is for the two exponents to equal \(0\) since \(3^0 = 1\) and \(5^0 = 1\)
If each exponent equals \(0\) then \(4x + 12 = 0\), which means \(x = -3\)
Now let's set the second exponent equal to \(0\) to get: \(3x+y = 0\)
If \(x = -3\), then the equation becomes: \(3(-3)+y = 0\)
Solve to get: \(y = 9\)
Answer: D
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Re: For integers x and y, 3^(4x+12)=5^(3x+y). What is the value of y? A.
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08 Sep 2022, 20:04
08 Sep 2022, 20:04
Given that For integers x and y, \(3^{(4x+12)}=5^{(3x+y)}\) and we need to find the value of y
Now 3 and 5 are prime numbers and their powers will be equal ONLY when value of both of them will be equal to 1, which happens at \(3^0\) and \(5^0\)
=> \(3^{(4x+12)}=5^{(3x+y)}\) = 1
=> 4x+12 = 0 and 3x + y = 0
=> 4x = -12
=> x = \(\frac{-12}{4}\) = -3
3x + y = 0
=> 3*-3 + y = 0
=> y - 9 = 0
=> y = 9
So, Answer will be D
Hope it helps!
Now 3 and 5 are prime numbers and their powers will be equal ONLY when value of both of them will be equal to 1, which happens at \(3^0\) and \(5^0\)
=> \(3^{(4x+12)}=5^{(3x+y)}\) = 1
=> 4x+12 = 0 and 3x + y = 0
=> 4x = -12
=> x = \(\frac{-12}{4}\) = -3
3x + y = 0
=> 3*-3 + y = 0
=> y - 9 = 0
=> y = 9
So, Answer will be D
Hope it helps!
