If 4^(n + 4) - 4^(n + 2) = 960, What is the value of n?

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19 May 2017 Root and Power

If 4^(n + 4) - 4^(n + 2) = 960, What is the value of n?

OPtion

1) 0
2) 3
3) 4
4) 1
5) -1
6) 2
7) -3
8) -2
9) -4
10) None of these

Solution

4^(n + 4) - 4^(n + 2) = 960

=> 4^(n + 2 + 2) - 4^(n + 2) = 960

=> 4^(n + 2) × 4^(2) - 4^(n + 2) = 960

=> 4^(n + 2)[4^(2) - 1] = 960

=> 4^(n + 2) × (15) = 960

=> 4^(n + 2) = 64
4^(n + 2) = 4^3
=> n + 2 = 3
=> n = 1

Correct Option: 4 Best Solution (7)