Step 1 :Given the equation \(2^{x}=38\)
Step 2 :Take the logarithm base 2 on both sides of the equation to solve for x. This gives us \(x = \log_2(38)\)
Step 3 :Using a calculator or a programming language like Python, we can calculate the exact value of \(x\), which is approximately 5.247927513443585
Step 4 :Rounding this value to 4 decimal places, we get \(x = 5.2479\)
Step 5 :\(\boxed{x = \log_2(38)}\) is the exact solution to the equation
Step 6 :\(\boxed{x = 5.2479}\) is the approximate solution to the equation to 4 decimal places