The following equation involves more than one exponential expression. Solve the equation. \[ 12^{x}=4^{x+2} \]

Solve the equation \( 12^{x}=4^{x+2} \). Solve the equation by following steps: - step0: Solve for \(x\): \(12^{x}=4^{x+2}\) - step1: Take the logarithm of both sides: \(\log_{4}{\left(12^{x}\right)}=\log_{4}{\left(4^{x+2}\right)}\) - step2: Evaluate the logarithm: \(\frac{x}{2}\log_{2}{\left(12\right)}=\frac{2\left(x+2\right)}{2}\) - step3: Rewrite the expression: \(\frac{x\log_{2}{\left(12\right)}}{2}=\frac{2\left(x+2\right)}{2}\) - step4: Multiply both sides of the equation by LCD: \(\frac{x\log_{2}{\left(12\right)}}{2}\times 2=\frac{2\left(x+2\right)}{2}\times 2\) - step5: Simplify the equation: \(\log_{2}{\left(12\right)}\times x=2x+4\) - step6: Move the variable to the left side: \(\log_{2}{\left(12\right)}\times x-2x=4\) - step7: Collect like terms: \(\left(\log_{2}{\left(12\right)}-2\right)x=4\) - step8: Divide both sides: \(\frac{\left(\log_{2}{\left(12\right)}-2\right)x}{\log_{2}{\left(12\right)}-2}=\frac{4}{\log_{2}{\left(12\right)}-2}\) - step9: Divide the numbers: \(x=\frac{4}{\log_{2}{\left(12\right)}-2}\) - step10: Simplify: \(x=\frac{4}{\log_{2}{\left(3\right)}}\) The solution to the equation \(12^{x}=4^{x+2}\) is \(x=\frac{4}{\log_{2}{(3)}}\).