If \( \log _{5}(-3 x+5)=3 \), then what is the value of \( x ? \)

To solve the equation \( \log _{5}(-3x + 5) = 3 \), follow these steps: 1. **Understand the Logarithmic Equation:** \[ \log_b A = C \quad \text{implies} \quad A = b^C \] Applying this to the given equation: \[ -3x + 5 = 5^3 \] 2. **Calculate the Exponent:** \[ 5^3 = 125 \] So, \[ -3x + 5 = 125 \] 3. **Solve for \( x \):** \[ -3x = 125 - 5 \] \[ -3x = 120 \] \[ x = \frac{120}{-3} \] \[ x = -40 \] 4. **Verify the Domain:** The argument of the logarithm must be positive: \[ -3x + 5 > 0 \] Substituting \( x = -40 \): \[ -3(-40) + 5 = 120 + 5 = 125 > 0 \] Thus, \( x = -40 \) is valid. **Final Answer:** \(\boxed{-40}\)