Solve for x 3e^(3x)=12

$3 e^{3 x} = 12$

Step 1

Divide each term in $3 e^{3 x} = 12$ by $3$ and simplify.

Divide each term in $3 e^{3 x} = 12$ by $3$ .

$\frac{3 e^{3 x}}{3} = \frac{12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 e^{3 x}}{3} = \frac{12}{3}$

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

$e^{3 x} = \frac{12}{3}$

Simplify the right side.

Divide $12$ by $3$ .

$e^{3 x} = 4$

Step 2

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

$\ln (e^{3 x}) = \ln (4)$

Step 3

Expand the left side.

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

$3 x \ln (e) = \ln (4)$

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

$3 x \cdot 1 = \ln (4)$

Multiply $3$ by $1$ .

$3 x = \ln (4)$

Step 4

Divide each term in $3 x = \ln (4)$ by $3$ and simplify.

Divide each term in $3 x = \ln (4)$ by $3$ .

$\frac{3 x}{3} = \frac{\ln (4)}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{\ln (4)}{3}$

Divide $x$ by $1$ .

$x = \frac{\ln (4)}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (4)}{3}$

Decimal Form:

$x = 0.46209812 \dots$