Solve for y e^y=2

$e^{y} = 2$

Step 1

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

$\ln (e^{y}) = \ln (2)$

Step 2

Expand the left side.

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

$y \ln (e) = \ln (2)$

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

$y \cdot 1 = \ln (2)$

Multiply $y$ by $1$ .

$y = \ln (2)$

Step 3

The result can be shown in multiple forms.

Exact Form:

$y = \ln (2)$

Decimal Form:

$y = 0.69314718 \dots$