If 2^x + 2^x + 2^x + 2^x = 2^n, what is x in terms of n?

Question

If  2^x + 2^x + 2^x + 2^x = 2^n , what is x in terms of n?

A. n/4
B. 4n
C. 2n
D. n - 2
E. n + 2

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ManifestDreamMBA · Answer

2^x + 2^x + 2^x + 2^x = 2^n 
 4 *2^x = 2^n 
 2^2 * 2^x = 2^n 
 2^{x+2} = 2^n

Equating exponents with same base
x+2 = n

x = n-2

Sketchitesh · Answer

4*2^x = 2 ^n  =>  2^2* 2^x = 2^n

2^{2+x}  =  2^n  => x = n-2

D is correct

NextstopISB · Answer

Question: 
If 2^x + 2^x + 2^x + 2^x = 2^n, what is x in terms of n?

Left-hand side: 
2^x + 2^x + 2^x + 2^x = 4 × 2^x

Recall: 
4 = 2^2

So: 
4 × 2^x = 2^2 × 2^x = 2^(x + 2)

Now set it equal to the right-hand side: 
2^(x + 2) = 2^n 
Therefore, x + 2 = n 
So, x = n - 2

Answer: D

Dereno · Answer

2^x + 2^x + 2^x + 2^x = 2^n

4 . 2^x = 2^n or

taking   2^x   common also yields the same result as above.

2^(x+2) = 2^n

equating powers, we get x+2 = n

Hence,  x = n-2

option D

Ayeka · Answer

2^x+2^x+2^x+2^x=2^n
4*2^x=2^n
(2^2)(2^x)=(2^n)
2^(2+x)=2^n
2+x=n
x=n-2

Answer: D

Abhiswarup · Answer

2^x+2^x+2^x+2^x=2^n
4*2^x=2^n
2^x+2=2^n
x+2=n
x=n-2

Answer is D

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