$2^{x}=8$

Step 1 ：Take the logarithm of both sides of the equation: \(\log_{2}(2^{x}) = \log_{2}(8)\)

Step 2 ：Apply the logarithm property: \(x \cdot \log_{2}(2) = \log_{2}(8)\)

Step 3 ：Simplify the equation: \(x = \log_{2}(8)\)

Step 4 ：Calculate the value of x: \(x = 3\)

Step 5 ：\(\boxed{x = 3}\)