Solve for x 1/3e^(4x)=12

$\frac{1}{3} e^{4 x} = 12$

Step 1

Multiply both sides of the equation by $3$ .

$3 (\frac{1}{3} \cdot e^{4 x}) = 3 \cdot 12$

Step 2

Simplify both sides of the equation.

Simplify the left side.

Simplify $3 (\frac{1}{3} \cdot e^{4 x})$ .

Combine $\frac{1}{3}$ and $e^{4 x}$ .

$3 \frac{e^{4 x}}{3} = 3 \cdot 12$

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{e^{4 x}}{3} = 3 \cdot 12$

Rewrite the expression.

$e^{4 x} = 3 \cdot 12$

Simplify the right side.

Multiply $3$ by $12$ .

$e^{4 x} = 36$

Step 3

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

$\ln (e^{4 x}) = \ln (36)$

Step 4

Expand the left side.

Expand $\ln (e^{4 x})$ by moving $4 x$ outside the logarithm.

$4 x \ln (e) = \ln (36)$

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

$4 x \cdot 1 = \ln (36)$

Multiply $4$ by $1$ .

$4 x = \ln (36)$

Step 5

Divide each term in $4 x = \ln (36)$ by $4$ and simplify.

Divide each term in $4 x = \ln (36)$ by $4$ .

$\frac{4 x}{4} = \frac{\ln (36)}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{\ln (36)}{4}$

Divide $x$ by $1$ .

$x = \frac{\ln (36)}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (36)}{4}$

Decimal Form:

$x = 0.89587973 \dots$