Solve the equation. Write the solution set with the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places.
\[
2^{x}=38
\]
Answer
\(\boxed{x = 5.2479}\) is the approximate solution to the equation to 4 decimal places
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
