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If 5^c-5^c-1
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05 Sep 2021, 14:57
05 Sep 2021, 14:57
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Expert Reply
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Question Stats:
92% (01:40) correct
7% (02:19) wrong based on 27 sessions
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If \(5^c-5^{c-1}=500\), then \(c(c-1)\)
(A) 72
(B) 30
(C) 20
(D) 12
(E) 6
(A) 72
(B) 30
(C) 20
(D) 12
(E) 6
Re: If 5^c-5^c-1
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05 Sep 2021, 18:21
05 Sep 2021, 18:21
2
Answer is (D) 12
5^c-5^c-1
5^c - 5^c / 5 = 500
5^c * (1 - 1/5) = 500
5^c * (4/5) = 500
5^c = 500 * 5/4 = 125*5 = 5^4
c = 4
therefore 4(4-1) = 4 * 3 = 12
5^c-5^c-1
5^c - 5^c / 5 = 500
5^c * (1 - 1/5) = 500
5^c * (4/5) = 500
5^c = 500 * 5/4 = 125*5 = 5^4
c = 4
therefore 4(4-1) = 4 * 3 = 12
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Re: If 5^c-5^c-1
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06 Sep 2021, 05:08
06 Sep 2021, 05:08
1
Carcass wrote:
If \(5^c-5^{c-1}=500\), then \(c(c-1)\)
(A) 72
(B) 30
(C) 20
(D) 12
(E) 6
(A) 72
(B) 30
(C) 20
(D) 12
(E) 6
Given: \(5^c-5^{c-1}=500\)
Factor out \(5^{c-1}\) to get: \(5^{c-1}(5 - 1)=500\)
Evaluate to get: \(5^{c-1}(4)=500\)
Divide both sides of the equation by \(4\) to get: \(5^{c-1}=125\)
Rewrite \(125\) as a power of \(5\): \(5^{c-1}=5^3\)
Since the bases are the same, the exponents must be equal: \(c-1=3\), which means \(c = 4\)
If \(c = 4\) lunch, then \(c(c-1)=4(4-1)=12\)
Answer: D
