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# If 5^(k + 1) = 2,000, what is the value of 5^k + 1?

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Joined: 02 Sep 2009
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If 5^(k + 1) = 2,000, what is the value of 5^k + 1?  [#permalink]

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26 Aug 2018, 06:31
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If $$5^{k + 1} = 2,000$$, what is the value of $$5^k + 1$$?

(A) 399
(B) 401
(C) 1,996
(D) 2,000
(E) 2,001

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Posts: 234
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Re: If 5^(k + 1) = 2,000, what is the value of 5^k + 1?  [#permalink]

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26 Aug 2018, 06:36
B?
$$5^k$$.5 = $$2^4$$.$$5^3$$

$$5^k$$= $$2^4$$.$$5^2$$ = 16 * 25 = 400

$$5^k$$ + 1 = 400 + 1 = 401
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Re: If 5^(k + 1) = 2,000, what is the value of 5^k + 1?  [#permalink]

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26 Aug 2018, 07:48
Bunuel wrote:
If $$5^{k + 1} = 2,000$$, what is the value of $$5^k + 1$$?

(A) 399
(B) 401
(C) 1,996
(D) 2,000
(E) 2,001

$$5^k*5 = 2^4*5^3$$

So, $$5^k = 2^4*5^2$$

Or, $$5^k = 400$$

So, $$5^k + 1 = 401$$ , Answer must be (B)
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Re: If 5^(k + 1) = 2,000, what is the value of 5^k + 1?  [#permalink]

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26 Aug 2018, 10:43
Bunuel wrote:
If $$5^{k + 1} = 2,000$$, what is the value of $$5^k + 1$$?

(A) 399
(B) 401
(C) 1,996
(D) 2,000
(E) 2,001

$$5^{k+1} = 2000$$
$$5^{k+1} = 2^45^3$$
$$5^k5 = 5^32^4$$
$$5^k = 5^22^4$$

$$5^2 = 25$$
$$2^4 = 16$$

25*16 = 400

$$5^k = 400$$

$$5^k$$ + 1 = 401.

The best answer is B.
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Re: If 5^(k + 1) = 2,000, what is the value of 5^k + 1?  [#permalink]

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26 Aug 2018, 11:53
Bunuel wrote:
If $$5^{k + 1} = 2,000$$, what is the value of $$5^k + 1$$?

(A) 399
(B) 401
(C) 1,996
(D) 2,000
(E) 2,001
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Re: If 5^(k + 1) = 2,000, what is the value of 5^k + 1?  [#permalink]

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26 Aug 2018, 22:56
Bunuel wrote:
If $$5^{k + 1} = 2,000$$, what is the value of $$5^k + 1$$?

(A) 399
(B) 401
(C) 1,996
(D) 2,000
(E) 2,001

$$5^{k + 1} = 2,000$$,

5^k . 5 = 2000,
5^k = 400

Therefore, 5^k + 1 = 400 + 1 = 401.

Hence answer is B.
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Re: If 5^(k + 1) = 2,000, what is the value of 5^k + 1?   [#permalink] 26 Aug 2018, 22:56
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# If 5^(k + 1) = 2,000, what is the value of 5^k + 1?

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