# How do you solve log_19(-5x-6)=log_19(2-3x)?

Jul 15, 2016

$x = - 4$

#### Explanation:

${\log}_{19} \left(- 5 x - 6\right) = {\log}_{19} \left(2 - 3 x\right)$

$\Leftrightarrow {\log}_{19} \left(- 5 x - 6\right) - {\log}_{19} \left(2 - 3 x\right) = 0$ or

${\log}_{19} \left(\frac{- 5 x - 6}{2 - 3 x}\right) = {\log}_{19} \left(1\right)$ or

$\frac{- 5 x - 6}{2 - 3 x} = 1$ or

$- 5 x - 6 = 2 - 3 x$ or

$- 5 x + 3 x = 2 + 6$ or $- 2 x = 8$

or $x = - \frac{8}{2} = - 4$

Jul 15, 2016

$x = - 4$

#### Explanation:

The log equation leads directly to a linear equation.

if $\log A = \log B , \text{ } \Rightarrow A = B$

$- 5 x - 6 = 2 - 3 x$

$- 6 - 2 = - 3 x + 5 x$

$- 8 = 2 x$

$- 4 = x$