# How do you find the domain of f(x)= ln(4x +3)?

Oct 22, 2017

$x > - \frac{3}{4}$

#### Explanation:

As $f \left(x\right) = \ln \left(4 x + 3\right)$ and we cannot have natural log of a negative number as also $0$, the domain is given by $4 x + 3 > 0$ or $x > - \frac{3}{4}$.

This may also be seen by the graph of $f \left(x\right) = \ln \left(4 x + 3\right)$

graph{ln(4x+3) [-10, 10, -5, 5]}

Oct 22, 2017

Write an inequality that asserts that the argument of the logarithm must be greater than zero and then solve for x.

#### Explanation:

Write the inequality

$4 x + 3 > 0$

Subtract 3 from both sides:

$4 x > - 3$

Divide both sides by 4:

$x > - \frac{3}{4}$

The domain is $\left\{x \in \mathbb{R} : x > - \frac{3}{4}\right\}$.