Question

What is the solution to this equation?

(1\4)+1
= 32
7
A. -1/2
B.
OC. 2
O D.
O A.
312
-2

Answer 1

`A)~ -\frac 72`

Explanation:

`~~~~~~~\left(\frac 14 \right)^(x+1) = 32\\\\\\\implies \left(\frac 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 = -\frac 72`