Question

question 12 (mandatory) (1 point) if $2^{x - 1}=\frac{1}{16}$, then $x$ is equal to
a) -4
b) -5
c) 5
d) -3

Explanation:

Step1: Rewrite the right - hand side

We know that $\frac{1}{16}=2^{- 4}$ since $a^{-n}=\frac{1}{a^{n}}$ and $2^4 = 16$. So the equation $2^{x - 1}=\frac{1}{16}$ becomes $2^{x - 1}=2^{-4}$.

Step2: Equate the exponents

If $a^m=a^n$, then $m = n$ for $a>0,a
eq1$. Here $a = 2$, so $x-1=-4$.

Step3: Solve for x

Add 1 to both sides of the equation $x - 1=-4$. We get $x=-4 + 1=-3$.

Answer:

D. -3