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Math Expert V
Joined: 02 Sep 2009
Posts: 58415
If 72^4 = (16)(6^n), what is the value of n?  [#permalink]

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Difficulty:   25% (medium)

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

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

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

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Joined: 09 Mar 2018
Posts: 995
Location: India
Re: If 72^4 = (16)(6^n), what is the value of n?  [#permalink]

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

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

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