Solve for x e^x=0.5

$e^{x} = 0.5$

Step 1

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

$\ln (e^{x}) = \ln (0.5)$

Step 2

Expand the left side.

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

$x \ln (e) = \ln (0.5)$

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

$x \cdot 1 = \ln (0.5)$

Multiply $x$ by $1$ .

$x = \ln (0.5)$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \ln (0.5)$

Decimal Form:

$x = - 0.69314718 \dots$