Solve for \( x \) \[ \log _{3}(-4 x+7)=3 \]

Solve the equation \( \log_{3}(-4x+7)=3 \). Solve the equation by following steps: - step0: Solve for \(x\): \(\log_{3}{\left(-4x+7\right)}=3\) - step1: Find the domain: \(\log_{3}{\left(-4x+7\right)}=3,x<\frac{7}{4}\) - step2: Convert the logarithm into exponential form: \(-4x+7=3^{3}\) - step3: Evaluate the power: \(-4x+7=27\) - step4: Move the constant to the right side: \(-4x=27-7\) - step5: Subtract the numbers: \(-4x=20\) - step6: Change the signs: \(4x=-20\) - step7: Divide both sides: \(\frac{4x}{4}=\frac{-20}{4}\) - step8: Divide the numbers: \(x=-5\) - step9: Check if the solution is in the defined range: \(x=-5,x<\frac{7}{4}\) - step10: Find the intersection: \(x=-5\) The solution to the equation \( \log_{3}(-4x+7)=3 \) is \( x=-5 \).