b) \( 3^{x} \cdot 4^{x-1}=\frac{1}{4} \cdot 144^{2-x} \)

Solve the equation \( 3^{x} \cdot 4^{x-1}=\frac{1}{4} \cdot 144^{2-x} \). Solve the equation by following steps: - step0: Solve for \(x\): \(3^{x}\times 4^{x-1}=\frac{1}{4}\times 144^{2-x}\) - step1: Rewrite the expression: \(12^{x}=144^{2-x}\) - step2: Rewrite the expression: \(12^{x}=12^{4-2x}\) - step3: Set the exponents equal: \(x=4-2x\) - step4: Move the variable to the left side: \(x+2x=4\) - step5: Add the terms: \(3x=4\) - step6: Divide both sides: \(\frac{3x}{3}=\frac{4}{3}\) - step7: Divide the numbers: \(x=\frac{4}{3}\) The solution to the equation \(3^{x} \cdot 4^{x-1}=\frac{1}{4} \cdot 144^{2-x}\) is \(x=\frac{4}{3}\) or \(x=1.\dot{3}\).