$\log (x + 3) = 1 + \log (5 - x)$$ \Rightarrow \log (x + 3) - \log (5 - x) = 1$ $ \Rightarrow \log \frac{{x + 3}}{{5 - x}} = 1 \Rightarrow {10^1} = \frac{{x + 3}}{{5 - x}}$$ \Rightarrow 50 - 10x = x + 3 \Rightarrow 50 - 3 = x + 10x$$ \Rightarrow 11x = 47 \Rightarrow x = \frac{{47}}{{11}}$