Precalculus Examples

$4 e^{- 3 x} = 108$

Step 1

Divide each term in $4 e^{- 3 x} = 108$ by $4$ and simplify.

Tap for more steps...

Step 1.1

Divide each term in $4 e^{- 3 x} = 108$ by $4$ .

$\frac{4 e^{- 3 x}}{4} = \frac{108}{4}$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 1.2.1.1

Cancel the common factor.

$\frac{4 e^{- 3 x}}{4} = \frac{108}{4}$

Step 1.2.1.2

Divide $e^{- 3 x}$ by $1$ .

$e^{- 3 x} = \frac{108}{4}$

Step 1.3

Simplify the right side.

Tap for more steps...

Step 1.3.1

Divide $108$ by $4$ .

$e^{- 3 x} = 27$

Step 2

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

$\ln (e^{- 3 x}) = \ln (27)$

Step 3

Expand the left side.

Tap for more steps...

Step 3.1

Expand $\ln (e^{- 3 x})$ by moving $- 3 x$ outside the logarithm.

$- 3 x \ln (e) = \ln (27)$

Step 3.2

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

$- 3 x \cdot 1 = \ln (27)$

Step 3.3

Multiply $- 3$ by $1$ .

$- 3 x = \ln (27)$

Step 4

Divide each term in $- 3 x = \ln (27)$ by $- 3$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $- 3 x = \ln (27)$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{\ln (27)}{- 3}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $- 3$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{\ln (27)}{- 3}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (27)}{- 3}$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Rewrite $\ln (27)$ as $\ln (3^{3})$ .

$x = \frac{\ln (3^{3})}{- 3}$

Step 4.3.2

Expand $\ln (3^{3})$ by moving $3$ outside the logarithm.

$x = \frac{3 \ln (3)}{- 3}$

Step 4.3.3

Cancel the common factor of $3$ and $- 3$ .

Tap for more steps...

Step 4.3.3.1

Factor $3$ out of $3 \ln (3)$ .

$x = \frac{3 (\ln (3))}{- 3}$

Step 4.3.3.2

Move the negative one from the denominator of $\frac{\ln (3)}{- 1}$ .

$x = - 1 \cdot \ln (3)$

Step 4.3.4

Rewrite $- 1 \ln (3)$ as $- \ln (3)$ .

$x = - \ln (3)$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \ln (3)$

Decimal Form:

$x = - 1.09861228 \dots$