Domain of log function

**jzellt** · November 9th 2009, 11:10 PM

How do I find the domain of log10 (x^2 - 4)?

**Bacterius** · November 10th 2009, 12:00 AM

What is the domain is the base 10 logarithm ? It is $0$ . Therefore, the domain of this function is :

$x^2 - 4 \geq 0$
$x^2 \geq 4$
$x \geq 2$ OR $x \leq -2$

Therefore, the domain of this function is $x \leq -2$ and $x \geq 2$

**Defunkt** · November 10th 2009, 12:26 AM

Originally Posted by Bacterius

What is the domain is the base 10 logarithm ? It is $0$ . Therefore, the domain of this function is :

$x^2 - 4 \geq 0$
$x^2 \geq 4$
$x \geq 2$ OR [tex]x \leq -2[\MATH]

Therefore, the domain of this function is $x \leq -2$ and $x \geq 2$

What is $log_{10}(0)$ ?

The restriction over the logarithmic function is that its argument (what is "inside" it) must be strictly positive. So in this case, the requirement is that $x^2-4 > 0 \Rightarrow |x| > 2 \Rightarrow x>2, x<-2$

**HallsofIvy** · November 10th 2009, 02:39 AM

Originally Posted by Bacterius

What is the domain is the base 10 logarithm ? It is $0$ .

Surely you mean "x> 0".

Therefore, the domain of this function is :

$x^2 - 4 \geq 0$
$x^2 \geq 4$
$x \geq 2$ OR [tex]x \leq -2[\MATH]

Therefore, the domain of this function is $x \leq -2$ and $x \geq 2$