# How do you solve -3e^(7a+9)+6=-6?

Oct 8, 2016

$3 {e}^{7 a + 9} + 6 = = - 6$ does not have any solution.

#### Explanation:

$3 {e}^{7 a + 9} + 6 = = - 6$

$\Leftrightarrow 3 {e}^{7 a + 9} = = - 6 - 6 = - 12$ and

${e}^{7 a + 9} = = - \frac{12}{3} = - 4$

But no power of $e$ can be negative, as for all $x ' s$, ${e}^{x}$ is positive.
graph{e^x [-10, 10, -5, 5]}

Hence, $3 {e}^{7 a + 9} + 6 = = - 6$ does not have any solution.