Solve for n -8.4e^(n+2.7)=-15

$- 8.4 e^{n + 2.7} = - 15$

Divide each term in $- 8.4 e^{n + 2.7} = - 15$ by $- 8.4$ and simplify.

Divide each term in $- 8.4 e^{n + 2.7} = - 15$ by $- 8.4$ .

$\frac{- 8.4 e^{n + 2.7}}{- 8.4} = \frac{- 15}{- 8.4}$

Simplify the left side.

Cancel the common factor of $- 8.4$ .

Cancel the common factor.

$\frac{- 8.4 e^{n + 2.7}}{- 8.4} = \frac{- 15}{- 8.4}$

Divide $e^{n + 2.7}$ by $1$ .

$e^{n + 2.7} = \frac{- 15}{- 8.4}$

Simplify the right side.

Divide $- 15$ by $- 8.4$ .

$e^{n + 2.7} = 1.7\overline{857142}$

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (e^{n + 2.7}) = \ln (1.7\overline{857142})$

Expand the left side.

Expand $\ln (e^{n + 2.7})$ by moving $n + 2.7$ outside the logarithm.

$(n + 2.7) \ln (e) = \ln (1.7\overline{857142})$

The natural logarithm of $e$ is $1$ .

$(n + 2.7) \cdot 1 = \ln (1.7\overline{857142})$

Multiply $n + 2.7$ by $1$ .

$n + 2.7 = \ln (1.7\overline{857142})$

Move all terms not containing $n$ to the right side of the equation.

Subtract $2.7$ from both sides of the equation.

$n = \ln (1.7\overline{857142}) - 2.7$

Subtract $2.7$ from $\ln (1.7\overline{857142})$ .

$n = - 2.1201815$