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If 7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 = 7^x, what is the value of

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If 7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 = 7^x, what is the value of  [#permalink]

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New post 19 Jul 2018, 01:39
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A
B
C
D
E

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Re: If 7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 = 7^x, what is the value of  [#permalink]

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New post 19 Jul 2018, 01:50
+1 for B.

7^9+7^9+7^9+7^9+7^9+7^9+7^9=7^x
7 * 7^9 = 7^x
7^10 = 7^x
x = 10

Hence, B.
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Re: If 7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 = 7^x, what is the value of  [#permalink]

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New post 19 Jul 2018, 02:49
Solution:

Solution



Approach and Working:
    • 7^9+7^9+7^9+7^9+7^9+7^9+7^9= 7^x
    • 7*7^9= 7^x
    • 7^10= 7^x
      o Hence, x= 10

Hence, the correct answer is option B.

Answer: B
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Re: If 7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 = 7^x, what is the value of  [#permalink]

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New post 19 Jul 2018, 03:54
Bunuel wrote:
If \(7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 = 7^x\), what is the value of x?


(A) 9

(B) 10

(C) 12

(D) 63

(E) 9^7



When ever we see these sums, if some integer is raised to some power, we require the # of terms to be equal to that integer..
1) say integer is 2.... 2^a+2^a=2*2^a=2^(a+1)
2) say integer is 3.... 3^a+3^a+3^a=3*3^a=3^(a+1)
So here to there are 7 terms of 7^9, sum of these will be 7*7^9=7^(9+1)=7^10

B
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Re: If 7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 = 7^x, what is the value of  [#permalink]

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New post 19 Jul 2018, 07:18
Bunuel wrote:
If \(7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 = 7^x\), what is the value of x?


(A) 9

(B) 10

(C) 12

(D) 63

(E) 9^7

\(7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 = 7^x\)

So, \(7^9 (1 + 1 + 1 + 1 + 1 + 1 + 1) = 7^x\)

Or, \(7^9 *7 = 7^x\)

Or, \(7^{10} = 7^x\)

So, \(x = 10\), Answer must be (B)
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Re: If 7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 = 7^x, what is the value of  [#permalink]

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New post 22 Jul 2018, 18:28
Bunuel wrote:
If \(7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 = 7^x\), what is the value of x?


(A) 9

(B) 10

(C) 12

(D) 63

(E) 9^7


We can simplify by factoring 7^9 from each term of the left hand side of the equation, obtaining:

7^9(1 + 1 + 1 + 1 + 1 + 1 + 1) = 7^x

7^9(7^1) = 7^x

7^10 = 7^x

10 = x

Answer: B
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Re: If 7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 = 7^x, what is the value of &nbs [#permalink] 22 Jul 2018, 18:28
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