For which of the following values of x is 4^x/x^4 an integer?

Question

For which of the following values of x is  \frac{4^x}{x^4}  an integer ?

I. 4
II. 6
III. 8

A. I only
B. III only
C. I and II only
D. I and III only
E. I, II and III

chetan2u · Answer

Substitute the values and check. 
I. 4..... clearly answer is 1....YES
II. 6...... The denominator has 3, while numerator does not. So it will be a fraction. 
III. 8.....  \frac{4^8}{8^4}=\frac{2^{16}}{2^{12}}=2^4 ...YES

D

Abhishek009 · Answer

I.  \frac{4^x}{x^4} = \frac{4^4}{4^4} = 1 
II.  \frac{4^x}{x^4} = \frac{4^6}{6^4} = \frac{2^{12}}{2^4*3^4} = \frac{2^{8}}{3^4} 
III.  \frac{4^x}{x^4} = \frac{4^8}{8^4} = \frac{2^{16}}{2^{12}} = 2^4

Thus, Answer must be D

EgmatQuantExpert · Answer

Solution

To find  
We need to determine
 • The values of x for which  \frac{4^x}{x^4}  is an integer

Approach and Working out  
Case I: x = 4
 •  \frac{4^x}{x^4}  = 1 = an integer

Case II: x = 6
 •  \frac{4^x}{x^4}  =  \frac{256}{81}  = not an integer

Case III: x = 8
 •  \frac{4^x}{x^4}  = 16 = an integer

Thus, Option D is the correct answer.

Correct Answer: Option D

For which of the following values of x is 4^x/x^4 an integer?

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For which of the following values of x is 4^x/x^4 an integer?

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