Solve for w -3*e^(5w)=-88

$- 3 \cdot e^{5 w} = - 88$

Step 1

Divide each term in $(- 3 \cdot e^{5 w}) = - 88$ by $- 3$ and simplify.

Divide each term in $(- 3 \cdot e^{5 w}) = - 88$ by $- 3$ .

$\frac{(- 3 \cdot e^{5 w})}{- 3} = \frac{- 88}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 \cdot e^{5 w}}{- 3} = \frac{- 88}{- 3}$

Divide $e^{5 w}$ by $1$ .

$e^{5 w} = \frac{- 88}{- 3}$

Simplify the right side.

Dividing two negative values results in a positive value.

$e^{5 w} = \frac{88}{3}$

Step 2

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

$\ln (e^{5 w}) = \ln (\frac{88}{3})$

Step 3

Expand the left side.

Expand $\ln (e^{5 w})$ by moving $5 w$ outside the logarithm.

$5 w \ln (e) = \ln (\frac{88}{3})$

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

$5 w \cdot 1 = \ln (\frac{88}{3})$

Multiply $5$ by $1$ .

$5 w = \ln (\frac{88}{3})$

Step 4

Divide each term in $5 w = \ln (\frac{88}{3})$ by $5$ and simplify.

Divide each term in $5 w = \ln (\frac{88}{3})$ by $5$ .

$\frac{5 w}{5} = \frac{\ln (\frac{88}{3})}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 w}{5} = \frac{\ln (\frac{88}{3})}{5}$

Divide $w$ by $1$ .

$w = \frac{\ln (\frac{88}{3})}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$w = \frac{\ln (\frac{88}{3})}{5}$

Decimal Form:

$w = 0.67574490 \dots$