If 2^n + 2^(n - 2) = 5120, what is the value of n ?

Question

If  2^n+2^{n-2}=5120, , what is the value of n ?
 
A. 8
B. 9 
C. 10 
D. 11 
E. 12

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Rabab36 · Answer

2^n +2^n-2=2^10*5

2^n(1+1/4)=2^10*5

2^n(5/4)=2^10*5

2^n-2*5==2^10*5

n-2=10
n=12

option E

gmatophobia · Answer

2^n+2^{n-2}=5120

2^{n-2}(2^{2}+1)=512 * 10

2^{n-2}(2^{2}+1)=2^9 * 2 * 5

2^{n-2}* 5 =2^{10} * 5

n - 2 = 10

n = 12

Option E

divyadna · Answer

2^n+ 2^n-2=5120
2^n + (2^n/2^2)= 5120

Take 2^n common
2^n(1+1/4)= 2^n(5/4)= 5120
2^n= 5120*4/5= 1024*4
2^n= 2^10*2^2
2^n= 2^12
n=12

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BhavikaA · Answer

2^n(1+1/4)= 2^n(5/4)= 5120

can you explain how you got 1/4 while takin 2^n as common?  Bunuel

sitipsa · Answer

Factoring our 2^n from 2^(n-2)

2^(n-2) =   
   =

If 2^n + 2^(n - 2) = 5120, what is the value of n ?

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GMAT Problem Solving (PS) Questions

If 2^n + 2^(n - 2) = 5120, what is the value of n ?

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