Precalculus Examples

$2 e^{3 x} = 1$

Step 1

Divide each term in $2 e^{3 x} = 1$ by $2$ and simplify.

Tap for more steps...

Step 1.1

Divide each term in $2 e^{3 x} = 1$ by $2$ .

$\frac{2 e^{3 x}}{2} = \frac{1}{2}$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.2.1.1

Cancel the common factor.

$\frac{2 e^{3 x}}{2} = \frac{1}{2}$

Step 1.2.1.2

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

$e^{3 x} = \frac{1}{2}$

Step 2

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

$\ln (e^{3 x}) = \ln (\frac{1}{2})$

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.

$3 x \ln (e) = \ln (\frac{1}{2})$

Step 3.2

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

$3 x \cdot 1 = \ln (\frac{1}{2})$

Step 3.3

Multiply $3$ by $1$ .

$3 x = \ln (\frac{1}{2})$

Step 4

Divide each term in $3 x = \ln (\frac{1}{2})$ by $3$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $3 x = \ln (\frac{1}{2})$ by $3$ .

$\frac{3 x}{3} = \frac{\ln (\frac{1}{2})}{3}$

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.

$\frac{3 x}{3} = \frac{\ln (\frac{1}{2})}{3}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (\frac{1}{2})}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (\frac{1}{2})}{3}$

Decimal Form:

$x = - 0.23104906 \dots$