To solve the logarithmic equation \( \log(x + 2) - \log(x - 1) = \log 2 \), use the property of logarithms that states \( \log a - \log b = \log \left(\frac{a}{b}\right) \):

\[ \log \left(\frac{x + 2}{x - 1}\right) = \log 2 \]

Since the logarithms are equal, the arguments must be equal:

\[ \frac{x + 2}{x - 1} = 2 \]

To solve for \( x \), multiply both sides by \( x - 1 \):

\[ x + 2 = 2(x - 1) \]

Expand and simplify:

\[ x + 2 = 2x - 2 \]
\[ 2 + 2 = 2x - x \]
\[ 4 = x \]

Thus, the value of \( x \) is:

C. 4