Answer
$x = 7$
Work Step by Step
To solve the given exponential equation, make the two sides have the same base. Then, equate the exponents and solve for the unknown variable.
Since $125=5^3$, the given equation is equivalent to:
$5^{4-x} = \dfrac{1}{5^3}$
Use the rule $\dfrac{1}{a^m} = a^{-m}$ to obtain:
$5^{4-x} = 5^{-3}$
Use the rule $a^m = a^n \longrightarrow m=n$ to obtain:
$4-x=-3$
Subtract $4$ to both sides to obtain:
$-x = -7$
Multiply $-1$ to both sides to obtain:
$x = 7$
