Linear Algebra Examples

$\log_{3} (x + 1) + \log_{3} (x - 1) = \log_{3} (2 x)$

Step 1

Set the argument in $\log_{3} (x + 1)$ greater than $0$ to find where the expression is defined.

$x + 1 > 0$

Step 2

Subtract $1$ from both sides of the inequality.

$x > - 1$

Step 3

Set the argument in $\log_{3} (x - 1)$ greater than $0$ to find where the expression is defined.

$x - 1 > 0$

Step 4

Add $1$ to both sides of the inequality.

$x > 1$

Step 5

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$(1, \infty)$

Set-Builder Notation:

${x | x > 1}$

Step 6