Solve the equation
\( 5^{(x − 2)} = (1 ÷ 125)^{(x +3)}\)
A
3/2
B
− 7/4
C
4/7
D
7/4
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\( 5^{(x − 2)} = (125^{−1} )^{(x + 3)}\\
5^{(x − 2)} = (5− 3)^{x + 3}\\
5^{(x − 2)} = 5^{− 3x − 9}\\
x + 3x = − 9 + 2\\
4x = − 7\\
x = \frac{−7}{4} \)
Source: Myschool Past Questions Archive (Record #41294)