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If 72^4 = (16)(6^n), what is the value of n?

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If 72^4 = (16)(6^n), what is the value of n?  [#permalink]

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New post 28 Jan 2019, 03:17
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A
B
C
D
E

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Question Stats:

74% (01:32) correct 26% (02:08) wrong based on 47 sessions

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Re: If 72^4 = (16)(6^n), what is the value of n?  [#permalink]

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New post 28 Jan 2019, 03:24
Bunuel wrote:
If \(72^4 = (16)(6^n)\), what is the value of n?

A. 2
B. 4
C. 6
D. 8
E. 10


IMO D

If \(72^4 = (16)(6^n)\)

\(2^{3*4} 3^{2*4} = 2^4 6^n\)

Compare the common bases

12 = 4+n

n = 8
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If 72^4 = (16)(6^n), what is the value of n?  [#permalink]

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New post 28 Jan 2019, 03:34
1
\((8*9)^4 = (2^4)3^n 2^n\)

\(2^{12} * 3^8 = 2^{4+n}*3^n\)

As bases are equal, compare either of the prime numbers power to another.

\(3^8 = 3^n\) or \(2^{12} = 2^{4+n}\)

n = 8

OPTION: D
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Re: If 72^4 = (16)(6^n), what is the value of n?  [#permalink]

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New post 28 Jan 2019, 04:01
Bunuel wrote:
If \(72^4 = (16)(6^n)\), what is the value of n?

A. 2
B. 4
C. 6
D. 8
E. 10


\(72^4 = 16 (6)^n\)

\(\frac{72*72 *72^2}{16} = 6^n\)

\(9*36*72^2 = 6^n\)

\(1296 = 6^n\)
\(6^n = 6^4\)

n = 4.

B is the correct answer.
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Re: If 72^4 = (16)(6^n), what is the value of n?  [#permalink]

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New post 28 Jan 2019, 05:12
Bunuel wrote:
If \(72^4 = (16)(6^n)\), what is the value of n?

A. 2
B. 4
C. 6
D. 8
E. 10



72^4= (2^4* 3*2)^4 = 2*12*3^8 = 16* 6^n
n= 8
IMO D
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Re: If 72^4 = (16)(6^n), what is the value of n?  [#permalink]

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New post 17 Feb 2019, 11:30
what is the value of n?

A. 2
B. 4
C. 6
D. 8
E. 10



72=(2^3)*(3^2), and 72^4=(2^12)*(3^8) which is equal to 16*6^n


thus 6^8=6^n or n=8, option D
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Re: If 72^4 = (16)(6^n), what is the value of n?   [#permalink] 17 Feb 2019, 11:30
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