Question

question 21 (mandatory) (1 point) if 2^{x - 1}=\frac{1}{16}, then x is equal to a) 5 b) - 5 c) - 4 d) - 3

Explanation:

Step1: Rewrite the right - hand side

Rewrite $\frac{1}{16}$ as a power of 2. Since $16 = 2^4$, then $\frac{1}{16}=2^{- 4}$. 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