# How do you solve -2*e^(8-6n)=-81.4?

Nov 16, 2017

Solution: $n \approx 0.715$

#### Explanation:

$- 2 \cdot {e}^{8 - 6 n} = - 81.4$ or

${e}^{8 - 6 n} = \frac{- 81.4}{-} 2 \mathmr{and} {e}^{8 - 6 n} = 40.7$

Taking natural log on both sides we get ,

$\left(8 - 6 n\right) = \ln \left(40.7\right) \left[\ln {e}^{x} = x\right]$

$8 - 6 n = 3.71 \mathmr{and} 6 n = 8 - 3.71 \mathmr{and} 6 n = 4.29$

$\therefore n = \frac{4.29}{6} \approx 0.715 \left(3 \mathrm{dp}\right)$

Solution: $n \approx 0.715$ [Ans]