+123 Solve the following exponential equations:
c. (4)^x-3 = 1/16
d. 3^x^2-42 = 1/3^x
f. x^2 2^x - 4(2^x) = 0
+9673 (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)
\(x^22^x-4(2^x)=0\\ 2^x(x^2-4)=0\\ 2^x(x-2)(x+2) =0\\ 2^x =0\text{(rejected) or } x = \pm 2\\ x = \pm 2\)
