If 4a + 4a+1 = 4a+2 - 176, what is the value of a ?

If 4^a + 4^a+1 = 4^a+2 - 176, what is the value of a ?

A 2

B 4

C 6

D 8

Correct Answer: Option A

Solution:

4^a + 4^a+1 = 4^a+2 - 176

=> 176 = 4^a+2 - 4^a - 4^a+1

=> 4^a \( \times \) 4² - 4^a - 4^a \( \times \) 4¹ = 176

=> 4^a \( \times \) 16 - 4^a - 4^a \( \times \) 4 = 176

=> 4^a (16 - 1 - 4) = 176

=> 4^a (16 - 5 ) = 176

=> 4^a \( \times \) 11 = 176

=> 4^a = 176/11

=> 4^a = 16

=> 4^a = 4²

a = 2.