Solve for x e^(3x)=12

$e^{3 x} = 12$

Step 1

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

$\ln (e^{3 x}) = \ln (12)$

Step 2

Expand the left side.

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

$3 x \ln (e) = \ln (12)$

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

$3 x \cdot 1 = \ln (12)$

Multiply $3$ by $1$ .

$3 x = \ln (12)$

Step 3

Divide each term in $3 x = \ln (12)$ by $3$ and simplify.

Divide each term in $3 x = \ln (12)$ by $3$ .

$\frac{3 x}{3} = \frac{\ln (12)}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{\ln (12)}{3}$

Divide $x$ by $1$ .

$x = \frac{\ln (12)}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (12)}{3}$

Decimal Form:

$x = 0.82830221 \dots$