Q. 11 - Calculus

Question

Moreover, the following properties follow from this definition (fill in the blanks or select the correct options):

$\ln x < 0$ on the interval ____, and $\ln x > 0$ on the interval ____.

Step-by-Step Solution

Answer

The complete statement is, 

$\ln x < 0$ on the interval $(0, 1)$, and $\ln x > 0$ on the interval $(1,\infty )$.

Step 1. Given information.

We are given an incomplete statement, 

$\ln x < 0$ on the interval ____, and $\ln x > 0$ on the interval ____.

Step 2. Completing the statement.

We know that the logarithmic function $\ln x < 0$ on the interval $(0, 1)$, and $\ln x > 0$ on the interval $(1,\infty )$.