# Question #7619b

##### 1 Answer
Jul 20, 2017

$\left(- \infty , 0\right)$

#### Explanation:

Range of $x - \left\lfloor x \right\rfloor$ is $\left[0 , 1\right)$

$0$ is not in the domain of $\ln$, and as $x$ gets close to $0$, $\ln x$ decreases without bound (goes to $- \infty$).

$\ln 1 = 0$, but $x - \left\lfloor x \right\rfloor$ never takes on the value $1$, so

the range of $\ln \left(x - \left\lfloor x \right\rfloor\right)$ is $\left(- \infty , 0\right)$