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If 5^(x + 1) − 5^x = 5^5(10^2), then what is the value of x?

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V
Joined: 02 Sep 2009
Posts: 47977
If 5^(x + 1) − 5^x = 5^5(10^2), then what is the value of x?  [#permalink]

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New post 31 Jul 2018, 21:48
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

88% (01:02) correct 12% (02:09) wrong based on 26 sessions

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Manager
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B
Joined: 17 Jan 2017
Posts: 137
Location: India
GPA: 4
WE: Information Technology (Computer Software)
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Re: If 5^(x + 1) − 5^x = 5^5(10^2), then what is the value of x?  [#permalink]

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New post 31 Jul 2018, 21:58
Bunuel wrote:
If \(5^{(x + 1)} − 5^x = 5^5(10^2)\), then what is the value of x?

A. 5
B. 6
C. 7
D. 8
E. 9


5^{(x + 1)} − 5^x = 5^5(10^2)
5^x.5^1 - 5^x = 5^5(5^2.2^2)
5^x(5^1-1) = 5^7.2^2
5^x.2^2 = 5^7.2^2
By equating, we get
x = 7

Hence, C
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Re: If 5^(x + 1) − 5^x = 5^5(10^2), then what is the value of x?  [#permalink]

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New post 31 Jul 2018, 21:59
+1 for C.

5^(x + 1) − 5^x = 5^5(10^2)
(5^x * 5) - 5^x = 5^5 * 5^2 * 2^2
5^x * ( 5 - 1) = 5^7 * 2^2
5^x * 2^2 = 5^7 * 2^2
5^x = 5^7
x = 7

Hence, C.
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If 5^(x + 1) − 5^x = 5^5(10^2), then what is the value of x?  [#permalink]

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New post 01 Aug 2018, 00:32
Bunuel wrote:
If \(5^{(x + 1)} − 5^x = 5^5(10^2)\), then what is the value of x?

A. 5
B. 6
C. 7
D. 8
E. 9



Given

\(5^{(x + 1)} − 5^x = 5^5(10^2)\)

\(5^x 5^1 - 5^x = 5^5 5^2 2^2\)

\(5^x(5 - 1 ) = 5^7 2^2\)

\(5^x *4 = 5^7 *4\)

\(5^x = 5^7\)

x = 7

The best answer is C.
If 5^(x + 1) − 5^x = 5^5(10^2), then what is the value of x? &nbs [#permalink] 01 Aug 2018, 00:32
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