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If 5^x - 5^{x-1}= 500 , what is the value of (x - 1)^2?
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22 Jul 2022, 06:31
22 Jul 2022, 06:31
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Question Stats:
66% (01:18) correct
33% (01:47) wrong based on 27 sessions
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If \(5^x - 5^{x-1}= 500\), what is the value of (x - 1)^2?
(A) 1
(B) 4
(C) 9
(D) 25
(E) 36
(A) 1
(B) 4
(C) 9
(D) 25
(E) 36
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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If 5^x - 5^{x-1}= 500 , what is the value of (x - 1)^2?
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22 Jul 2022, 06:40
22 Jul 2022, 06:40
2
Carcass wrote:
If \(5^x - 5^{x-1}= 500\), what is the value of \((x - 1)^2\)?
(A) 1
(B) 4
(C) 9
(D) 25
(E) 36
(A) 1
(B) 4
(C) 9
(D) 25
(E) 36
Given: \(5^x - 5^{x-1}= 500\)
Factor out the greatest common divisor: \(5^{x-1}(5^1 - 1)= 500\)
Evaluate the part in brackets: \(5^{x-1}(4)= 500\)
Divide both sides by \(4\) to get: \(5^{x-1}= 125\)
Rewrite the right side as a power of \(5\) to get: \(5^{x-1}= 5^3\)
Since the bases are equal, we can conclude that: \(x-1= 3\), which means \(x = 4\)
If \(x = 4\), then \((x - 1)^2 = (4 - 1)^2 = 3^2 = 9\)
Answer: C
Re: If 5^x - 5^{x-1}= 500 , what is the value of (x - 1)^2?
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23 Jul 2022, 00:45
23 Jul 2022, 00:45
1
In the Question, it is given :
5^x - 5^(x-1)=500
Factor out 5^x –
=> 5^x * (1- 1/5) = 500
=> 5^x * (4/5) = 500
=> 5^x = (500 * 5)/4 = (250 * 5)/2 = 5^4
Therefore, x = 4
So, (x-1)^2 = (4-1)^2 = (3)^2 = 9
Correct Answer: C
5^x - 5^(x-1)=500
Factor out 5^x –
=> 5^x * (1- 1/5) = 500
=> 5^x * (4/5) = 500
=> 5^x = (500 * 5)/4 = (250 * 5)/2 = 5^4
Therefore, x = 4
So, (x-1)^2 = (4-1)^2 = (3)^2 = 9
Correct Answer: C
