Solve for n -e^(-3.9n-1)-1=-3

$- e^{- 3.9 n - 1} - 1 = - 3$

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

Add $1$ to both sides of the equation.

$- e^{- 3.9 n - 1} = - 3 + 1$

Add $- 3$ and $1$ .

$- e^{- 3.9 n - 1} = - 2$

Divide each term in $- e^{- 3.9 n - 1} = - 2$ by $- 1$ and simplify.

Divide each term in $- e^{- 3.9 n - 1} = - 2$ by $- 1$ .

$\frac{- e^{- 3.9 n - 1}}{- 1} = \frac{- 2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{e^{- 3.9 n - 1}}{1} = \frac{- 2}{- 1}$

Divide $e^{- 3.9 n - 1}$ by $1$ .

$e^{- 3.9 n - 1} = \frac{- 2}{- 1}$

Simplify the right side.

Divide $- 2$ by $- 1$ .

$e^{- 3.9 n - 1} = 2$

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

$\ln (e^{- 3.9 n - 1}) = \ln (2)$

Expand the left side.

Expand $\ln (e^{- 3.9 n - 1})$ by moving $- 3.9 n - 1$ outside the logarithm.

$(- 3.9 n - 1) \ln (e) = \ln (2)$

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

$(- 3.9 n - 1) \cdot 1 = \ln (2)$

Multiply $- 3.9 n - 1$ by $1$ .

$- 3.9 n - 1 = \ln (2)$

Add $1$ to both sides of the equation.

$- 3.9 n = \ln (2) + 1$

Divide each term in $- 3.9 n = \ln (2) + 1$ by $- 3.9$ and simplify.

Divide each term in $- 3.9 n = \ln (2) + 1$ by $- 3.9$ .

$\frac{- 3.9 n}{- 3.9} = \frac{\ln (2)}{- 3.9} + \frac{1}{- 3.9}$

Simplify the left side.

Cancel the common factor of $- 3.9$ .

Cancel the common factor.

$\frac{- 3.9 n}{- 3.9} = \frac{\ln (2)}{- 3.9} + \frac{1}{- 3.9}$

Divide $n$ by $1$ .

$n = \frac{\ln (2)}{- 3.9} + \frac{1}{- 3.9}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$n = - \frac{\ln (2)}{3.9} + \frac{1}{- 3.9}$

Replace $e$ with an approximation.

$n = - \frac{\log_{2.71828182} (2)}{3.9} + \frac{1}{- 3.9}$

Log base $2.71828182$ of $2$ is approximately $0.69314718$ .

$n = - \frac{0.69314718}{3.9} + \frac{1}{- 3.9}$

Divide $0.69314718$ by $3.9$ .

$n = - 1 \cdot 0.17773004 + \frac{1}{- 3.9}$

Multiply $- 1$ by $0.17773004$ .

$n = - 0.17773004 + \frac{1}{- 3.9}$

Divide $1$ by $- 3.9$ .

$n = - 0.17773004 - 0.\overline{256410}$

Subtract $0.\overline{256410}$ from $- 0.17773004$ .

$n = - 0.4341403$

Solve for n -e^(-3.9n-1)-1=-3

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