# How do you solve -e^(6-9p)+5=-48.4?

Nov 27, 2016

$p = \frac{1}{9} \ln 53.4 - \frac{2}{3}$

$p \approx - .2247$

#### Explanation:

$- {e}^{6 - 9 p} + 5 = - 48.4$

Subtract $5$ from each side:
$- {e}^{6 - 9 p} = - 53.4$

Divide each side by $- 1$:
${e}^{6 - 9 p} = 53.4$

Rewrite as a natural log:
$\ln 53.4 = 6 - 9 p$

Solve for p -- subtract 6 from each side:
$\ln 53.4 - 6 = 9 p$

Divide each side by 9:
$\frac{\ln 53.4 - 6}{9} = p$

Simplify:
$p = \frac{1}{9} \ln 53.4 - \frac{2}{3}$