Given: \(\frac{d}{dx}(f(x)) = \log x\)

We need to find \(f(x)\), which means we need to integrate \(\log x\) with respect to \(x\).

So, \(f(x) = \int \log x \, dx\)

We can use integration by parts, which states: \(\int u \, dv = uv - \int v \, du\)

Let \(u = \log x\) and \(dv = dx\)

Then, \(du = \frac{1}{x} \, dx\) and \(v = x\)

Applying integration by parts:

\(f(x) = \int \log x \, dx = x \log x - \int x \cdot \frac{1}{x} \, dx\)

\(f(x) = x \log x - \int 1 \, dx\)

\(f(x) = x \log x - x + C\)

\(f(x) = x (\log x - 1) + C\)