Calculus Examples

$3 e^{x} - 2 = 0$

Step 1

Add $2$ to both sides of the equation.

$3 e^{x} = 2$

Step 2

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

Tap for more steps...

Step 2.1

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

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

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

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

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

Step 3

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

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

Step 4

Expand the left side.

Tap for more steps...

Step 4.1

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

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

Step 4.2

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

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

Step 4.3

Multiply $x$ by $1$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.40546510 \dots$