# How do you solve log (-2a+9)=log(7-4a)?

Nov 4, 2016

Set the expressions equal to find $a = - 1$

#### Explanation:

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

If the log of an expression equals the log of another expression, the two expressions must be equal.

$- 2 a + 9 = 7 - 4 a$
$+ 4 a \textcolor{w h i t e}{a a a a {a}^{22} a} + 4 a$

$\textcolor{w h i t e}{{a}^{2}} 2 a + 9 = \textcolor{w h i t e}{a a} 7$
$\textcolor{w h i t e}{a {a}^{2} a} - 9 = - 9$

$\textcolor{w h i t e}{{a}^{2}} \frac{2 a}{2} = \frac{- 2}{2}$

$\textcolor{w h i t e}{a a {a}^{2}} a = - 1$