Solve for x natural log of 3x-3 = natural log of x-6

$\ln (3 x - 3) = \ln (x - 6)$

Step 1

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$3 x - 3 = x - 6$

Step 2

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $x$ from both sides of the equation.

$3 x - 3 - x = - 6$

Subtract $x$ from $3 x$ .

$2 x - 3 = - 6$

Move all terms not containing $x$ to the right side of the equation.

Add $3$ to both sides of the equation.

$2 x = - 6 + 3$

Add $- 6$ and $3$ .

$2 x = - 3$

Divide each term in $2 x = - 3$ by $2$ and simplify.

Divide each term in $2 x = - 3$ by $2$ .

$\frac{2 x}{2} = \frac{- 3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 3}{2}$

Divide $x$ by $1$ .

$x = \frac{- 3}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{3}{2}$

Step 3

Exclude the solutions that do not make $\ln (3 x - 3) = \ln (x - 6)$ true.

$No solution$