Solve for \( x \) : \( 4^{x}=38 \) \( x=\square \) You may enter the exact value or round to 4 decimal places. Question Help: Video

Solve the equation \( 4^{x}=38 \). Solve the equation by following steps: - step0: Solve for \(x\): \(4^{x}=38\) - step1: Take the logarithm of both sides: \(\log_{4}{\left(4^{x}\right)}=\log_{4}{\left(38\right)}\) - step2: Evaluate the logarithm: \(x=\log_{4}{\left(38\right)}\) - step3: Simplify: \(x=\frac{\log_{2}{\left(38\right)}}{2}\) - step4: Calculate: \(x=\frac{1+\log_{2}{\left(19\right)}}{2}\) The solution to the equation \(4^{x}=38\) is \(x \approx 2.623964\).