# How do you solve ln(1-8n)-10=-7?

Jun 13, 2018

$n = \frac{1 - {e}^{3}}{8} \approx - 2.386$

#### Explanation:

$\ln \left(1 - 8 n\right) - 10 = - 7$

$\ln \left(1 - 8 n\right) = 3$

$1 - 8 n = {e}^{3}$

$8 n = 1 - {e}^{3}$

$n = \frac{1 - {e}^{3}}{8} \approx - 2.386$

Jun 13, 2018

$n = \setminus \frac{1 - {e}^{3}}{8}$

#### Explanation:

Add $10$ to both sides:

$\ln \left(1 - 8 n\right) = 3$

Consider both sides as exponents of $e$:

${e}^{\ln \left(1 - 8 n\right)} = {e}^{3}$

$\setminus \therefore 1 - 8 n = {e}^{3}$

Subtract $1$ from both sides

$- 8 n = {e}^{3} - 1$

Divide both sides by $- 8$:

$n = \setminus \frac{1 - {e}^{3}}{8}$