We have to solve the equation 1/2^(x^2-1) = sqrt (16^x)
1/2^(x^2-1) = sqrt (16^x)
=> 2^-(x^2 - 1) = 16^x^(1/2)
=> 2^(-x^2 + 1) = 2^4^x^(1/2)
=> 2^(-x^2 + 1) = 2^2x
We can equate the exponent as the base is the same
-x^2 + 1 = 2x
=> x^2...
See This Answer Now
Start your subscription to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Already a member? Log in here.
We have to solve the equation 1/2^(x^2-1) = sqrt (16^x)
1/2^(x^2-1) = sqrt (16^x)
=> 2^-(x^2 - 1) = 16^x^(1/2)
=> 2^(-x^2 + 1) = 2^4^x^(1/2)
=> 2^(-x^2 + 1) = 2^2x
We can equate the exponent as the base is the same
-x^2 + 1 = 2x
=> x^2 + 2x - 1 = 0
x1 = [-2 + sqrt (4 + 4)]/2
=> x1 = -1 + sqrt 2
x2 = -1 - sqrt 2
The required solution is x = -1 + sqrt 2 and x = -1 - sqrt 2.