Answer:
[tex]A)~ -\dfrac 72[/tex]
Step-by-step explanation:
[tex]~~~~~~~\left(\dfrac 14 \right)^{x+1} = 32\\\\\\\implies \left(\dfrac 1{2^2} \right)^{x+1} = 2^5\\\\\\\implies \left( 2^{-2} \right)^{x+1} = 2^5\\\\\\\implies 2^{-2(x+1)} = 2^5\\\\\\\implies 2^{-2x-2} = 2^5\\\\\\\implies -2x -2 = 5\\\\\\\implies -2x = 5+2\\\\\\\implies -2x = 7\\\\\\\implies x = -\dfrac 72[/tex]
