We have to determine the value of x for the equation: 4^(x^2+x) - 4096 = 0.

4^(x^2+x) - 4096 = 0

=> 4^(x^2+x) = 4096

=> 4^(x^2+x) = 4096

=> 4^(x^2+x) = 4^6

As the base is equal, equate the exponent

=> x^2 + x = 6

=> x^2 +...

## See

This Answer NowStart your **48-hour free trial** to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Already a member? Log in here.

We have to determine the value of x for the equation: 4^(x^2+x) - 4096 = 0.

4^(x^2+x) - 4096 = 0

=> 4^(x^2+x) = 4096

=> 4^(x^2+x) = 4096

=> 4^(x^2+x) = 4^6

As the base is equal, equate the exponent

=> x^2 + x = 6

=> x^2 + 3x - 2x - 6 = 0

=> x(x + 3) - 2(x + 3) = 0

=> (x - 2)(x + 3) = 0

=> x = 2 and x = -3

**The required values are x = 2 and x = -3**