Question

Determine the roots of the function f(x) = (5^2x − 6)^2 − (5^2x − 6) − 12.please i want it within 2 days......

Answer 1

Answer:

$let \: {5}^{2x} - 6 = y \\ so \:equation \: become \\ {y}^{2} - y - 12 = 0 \\ {y}^{2} - 4y + 3y - 12 = 0 \\ y(y - 4) + 3(y - 4) = 0 \\ (y - 4)(y + 3) = 0 \\ y = 4 \: or \: y = - 3\\ so \: {5}^{2x } - 6 = 4 \\ {5}^{2x} = 10 \\ 2x log(5) = 1 \\ x = \frac{1}{2log5} \\ now \: y = - 3 \\ {5}^{2x} - 6 = - 3 \\ {5}^{2x} = 3 \\ 2x log(5) = log(3) \\ x = \frac{ log(3) }{2 log(5) }$

Answer 2

Answer:

this is correct................