# How do you find the domain of log(3x^2-4x+5)?

Jun 20, 2016

The domain is $\mathbb{R}$

#### Explanation:

It must be:

$3 {x}^{2} - 4 x + 5 > 0$

let's find the zeroes of the trynomial:

$x = \frac{2 \pm \sqrt{4 - 15}}{3}$

Since the expression under square root is negative,
the disequation
$3 {x}^{2} - 4 x + 5 > 0$
is verified for all x in $\mathbb{R}$