Solve for x e^(-3.3x)-7.6=26

$e^{- 3.3 x} - 7.6 = 26$

Step 1

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

Add $7.6$ to both sides of the equation.

$e^{- 3.3 x} = 26 + 7.6$

Add $26$ and $7.6$ .

$e^{- 3.3 x} = 33.6$

Step 2

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

$\ln (e^{- 3.3 x}) = \ln (33.6)$

Step 3

Expand the left side.

Expand $\ln (e^{- 3.3 x})$ by moving $- 3.3 x$ outside the logarithm.

$- 3.3 x \ln (e) = \ln (33.6)$

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

$- 3.3 x \cdot 1 = \ln (33.6)$

Multiply $- 3.3$ by $1$ .

$- 3.3 x = \ln (33.6)$

Step 4

Divide each term in $- 3.3 x = \ln (33.6)$ by $- 3.3$ and simplify.

Divide each term in $- 3.3 x = \ln (33.6)$ by $- 3.3$ .

$\frac{- 3.3 x}{- 3.3} = \frac{\ln (33.6)}{- 3.3}$

Simplify the left side.

Cancel the common factor of $- 3.3$ .

Cancel the common factor.

$\frac{- 3.3 x}{- 3.3} = \frac{\ln (33.6)}{- 3.3}$

Divide $x$ by $1$ .

$x = \frac{\ln (33.6)}{- 3.3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{\ln (33.6)}{3.3}$

Replace $e$ with an approximation.

$x = - \frac{\log_{2.71828182} (33.6)}{3.3}$

Log base $2.71828182$ of $33.6$ is approximately $3.51452606$ .

$x = - \frac{3.51452606}{3.3}$

Divide $3.51452606$ by $3.3$ .

$x = - 1 \cdot 1.06500789$

Multiply $- 1$ by $1.06500789$ .

$x = - 1.06500789$