Domain of log function

jzellt · #1 $Old$ November 10th, 2009, 12:10 AM

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

Bacterius · #2 $Old$ November 10th, 2009, 01:00 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 · #3 $Old$ November 10th, 2009, 01:26 AM

Quote:

Originally Posted by Bacterius $View Post$

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 [math]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 · #4 $Old$ November 10th, 2009, 03:39 AM

Quote:

Originally Posted by Bacterius $View Post$

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

Surely you mean "x> 0".

Quote:

Therefore, the domain of this function is :

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

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

Bacterius · #5 $Old$ November 10th, 2009, 11:42 AM

Yes sorry I meant $x \geq 0$ .

Defunkt · #6 $Old$ November 10th, 2009, 01:46 PM

Quote:

Originally Posted by Bacterius $View Post$

Yes sorry I meant $x \geq 0$ .

Again, $x>0$ , not $\geq$ :P

Bacterius · #7 $Old$ November 10th, 2009, 05:30 PM

Oh my mistake, sorry. It is indeed $x > 0$