Solve for y 3=e^(4y)

$3 = e^{4 y}$

Step 1

Rewrite the equation as $e^{4 y} = 3$ .

$e^{4 y} = 3$

Step 2

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

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

Step 3

Expand the left side.

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

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

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

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

Multiply $4$ by $1$ .

$4 y = \ln (3)$

Step 4

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

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

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = 0.27465307 \dots$