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If (5^(5x))(25) = 5^n when n and x are integers, what is the value of

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Bunuel
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If (5^(5x))(25) = 5^n when n and x are integers, what is the value of [#permalink] New post   24 May 2018, 05:49
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If \((5^{5x})(25)=5^n\) when n and x are integers, what is the value of n in terms of x ?

A. 5x + 1

B. 5x + 2

C. 5x + 5

D. 10x

E. 10x + 2
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B
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Re: If (5^(5x))(25) = 5^n when n and x are integers, what is the value of [#permalink] New post   24 May 2018, 06:07
Bunuel wrote:
If \((5^{5x})(25)=5^n\) when n and x are integers, what is the value of n in terms of x ?

A. 5x + 1

B. 5x + 2

C. 5x + 5

D. 10x

E. 10x + 2


\((5^{5x})(5^2)=5^n\)
\((5^{5x + 2})=5^n\)
Equating the powers because the bases are the same, we get 5x + 2 = n
Choice B
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Re: If (5^(5x))(25) = 5^n when n and x are integers, what is the value of [#permalink] New post   24 May 2018, 07:22
Bunuel wrote:
If \((5^{5x})(25)=5^n\) when n and x are integers, what is the value of n in terms of x ?

A. 5x + 1

B. 5x + 2

C. 5x + 5

D. 10x

E. 10x + 2

\((5^{5x})(25)=5^n\)

Or, \(5^{5x+2}=5^n\)

So, \(n = 5x + 2\), Answer must be (B)
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Re: If (5^(5x))(25) = 5^n when n and x are integers, what is the value of [#permalink] New post   25 May 2018, 09:53
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Solution



Given:
• \((5^{5x}) (25) = 5^n\) where n and x are integers

To find:
• The value of n in terms of x

Approach and Working:
• From the given expression \((5^{5x}) (25) = 5^n\), we can rewrite it as
    \((5^{5x}) (5^2) = 5^n\)
    Or, \(5^{(5x + 2)} = 5^n\)
Comparing the base values on both sides, we can write
    5x + 2 = n

Hence, the correct answer is option B.

Answer: B
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Re: If (5^(5x))(25) = 5^n when n and x are integers, what is the value of [#permalink] New post   28 May 2018, 19:39
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Bunuel wrote:
If \((5^{5x})(25)=5^n\) when n and x are integers, what is the value of n in terms of x ?

A. 5x + 1

B. 5x + 2

C. 5x + 5

D. 10x

E. 10x + 2


We re-express 25 as 5^2 to obtain:

(5^5x)(5^2) = 5^n

5^(5x + 2) = 5^n

5x + 2 = n

Answer: B
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Re: If (5^(5x))(25) = 5^n when n and x are integers, what is the value of [#permalink] New post   03 Jun 2018, 04:40
Bunuel wrote:
If \((5^{5x})(25)=5^n\) when n and x are integers, what is the value of n in terms of x ?

A. 5x + 1

B. 5x + 2

C. 5x + 5

D. 10x

E. 10x + 2



\((5^{5x})(25)=5^n\)

\((5^{5x})(5^2)=5^n\)

\(5^{5x+2}\) = \(5^n\) equate bases

\(5x+2=n\) :-)
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Re: If (5^(5x))(25) = 5^n when n and x are integers, what is the value of [#permalink]
03 Jun 2018, 04:40
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