I need help with solving the equations please.

(c)

$4^{x-3} = \dfrac{1}{16}\\ 4^{x-3} = 4^{-2}\\ x -3=-2\\ x=1$

(d)

$3^{x^2-42} = \left(\dfrac{1}3\right)^x\\ 3^{x^2-42} = 3^{-x}\\ x^2-42=-x\\ x^2+x-42=0\\ (x+7)(x-6)=0\\ x = -7\text{ or }x=6$

(f)

$x^22^x-4(2^x)=0\\ 2^x(x^2-4)=0\\ 2^x(x-2)(x+2) =0\\ 2^x =0\text{(rejected) or } x = \pm 2\\ x = \pm 2$