To solve the equation \(2^x = 3\), we can use logarithms to change the exponentiation to a multiplication. Specifically, we can use the logarithm base 2, written as \(\log_2\), to change \(2^x \) to \(x \times \log_2(2)\).

So,

\[2^x = 3\]

can be rewritten as

\[x \times \log_2(2) = \log_2(3)\]

To solve for \(x\), we divide both sides by \(\log_2(2)\)

\[x = \log_2(3)\]

\(\log_2(3)\) is approximately \(1.5849625007211563\).

So the final solution for \(x\) is \(x = 1.5849625007211563\)