Domain of log function

• Nov 9th 2009, 11:10 PM
jzellt
Domain of log function
How do I find the domain of log10 (x^2 - 4)?
• Nov 10th 2009, 12:00 AM
Bacterius
What is the domain is the base 10 logarithm ? It is $\displaystyle 0$. Therefore, the domain of this function is :

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

Therefore, the domain of this function is $\displaystyle x \leq -2$ and $\displaystyle x \geq 2$
• Nov 10th 2009, 12:26 AM
Defunkt
Quote:

Originally Posted by Bacterius
What is the domain is the base 10 logarithm ? It is $\displaystyle 0$. Therefore, the domain of this function is :

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

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

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

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 $\displaystyle x^2-4 > 0 \Rightarrow |x| > 2 \Rightarrow x>2, x<-2$
• Nov 10th 2009, 02:39 AM
HallsofIvy
Quote:

Originally Posted by Bacterius
What is the domain is the base 10 logarithm ? It is $\displaystyle 0$.

Surely you mean "x> 0".

Quote:

Therefore, the domain of this function is :

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

Therefore, the domain of this function is $\displaystyle x \leq -2$ and $\displaystyle x \geq 2$
• Nov 10th 2009, 10:42 AM
Bacterius
Yes sorry I meant $\displaystyle x \geq 0$.
• Nov 10th 2009, 12:46 PM
Defunkt
Quote:

Originally Posted by Bacterius
Yes sorry I meant $\displaystyle x \geq 0$.

Again, $\displaystyle x>0$, not $\displaystyle \geq$ :P
• Nov 10th 2009, 04:30 PM
Bacterius
Oh my mistake, sorry. It is indeed $\displaystyle x > 0$ (Speechless)