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.
We’ll help your grades soar
Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.
- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support
Already a member? Log in here.
Are you a teacher? Sign up now