# How do you solve ln(3x-1)=ln x and find any extraneous solutions?

Jul 4, 2016

$x = \frac{1}{2}$

#### Explanation:

The equation is equivalent to the following sentences:

$3 x - 1 \ge 0 \mathmr{and} x \ge 0 \mathmr{and} 3 x - 1 = x$

$x > \frac{1}{3} \mathmr{and} x \ge 0 \mathmr{and} 2 x = 1$

$x > \frac{1}{3} \mathmr{and} x = \frac{1}{2}$

$x = \frac{1}{2}$