Question

1. solve for x.

$5^{2-x}=\frac{1}{125}$
options:
$x=\frac{5}{3}$
$x=-1$
$x=\frac{7}{3}$
$x=5$

Explanation:

Step1: Rewrite RHS as power of 5

$\frac{1}{125} = 5^{-3}$

Step2: Set exponents equal

Since $5^{2-x}=5^{-3}$, equate exponents:
$2-x = -3$

Step3: Solve for x

Rearrange to isolate $x$:
$x = 2 + 3$

Answer:

$\boldsymbol{x=5}$ (corresponding to the option: $\boldsymbol{x=5}$)