Answer
By substituting $y = 1$, we can disprove the equality between both sides of the equal sign.
Work Step by Step
(a) $$\ln{(x-y)} = \ln x - \ln y$$ $$\ln(x - 1) = \ln x - \ln(1)$$ $$\ln(x - 1) = \ln x - 0$$ $$\ln(x - 1) \neq \ln x$$
(b) $\ln (x-1)$ is the blue line; $\ln x$ is the green line.