Solve for x log of 9-x = log of 2x-6

$\log (9 - x) = \log (2 x - 6)$

Step 1

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

$9 - x = 2 x - 6$

Step 2

Solve for $x$ .

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

Subtract $2 x$ from both sides of the equation.

$9 - x - 2 x = - 6$

Subtract $2 x$ from $- x$ .

$9 - 3 x = - 6$

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

Subtract $9$ from both sides of the equation.

$- 3 x = - 6 - 9$

Subtract $9$ from $- 6$ .

$- 3 x = - 15$

Divide each term in $- 3 x = - 15$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 15$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 15}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 15}{- 3}$

Divide $x$ by $1$ .

$x = \frac{- 15}{- 3}$

Simplify the right side.

Divide $- 15$ by $- 3$ .

$x = 5$