Solve for a log of -2a+9 = log of 7-4a

$\log (- 2 a + 9) = \log (7 - 4 a)$

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

$- 2 a + 9 = 7 - 4 a$

Solve for $a$ .

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

Add $4 a$ to both sides of the equation.

$- 2 a + 9 + 4 a = 7$

Add $- 2 a$ and $4 a$ .

$2 a + 9 = 7$

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

Subtract $9$ from both sides of the equation.

$2 a = 7 - 9$

Subtract $9$ from $7$ .

$2 a = - 2$

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

Divide each term in $2 a = - 2$ by $2$ .

$\frac{2 a}{2} = \frac{- 2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 a}{2} = \frac{- 2}{2}$

Divide $a$ by $1$ .

$a = \frac{- 2}{2}$

Simplify the right side.

Divide $- 2$ by $2$ .

$a = - 1$