Solve for x e^x+3=8

$e^{x} + 3 = 8$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$e^{x} = 8 - 3$

Subtract $3$ from $8$ .

$e^{x} = 5$

Step 2

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

$\ln (e^{x}) = \ln (5)$

Step 3

Expand the left side.

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

$x \ln (e) = \ln (5)$

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

$x \cdot 1 = \ln (5)$

Multiply $x$ by $1$ .

$x = \ln (5)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \ln (5)$

Decimal Form:

$x = 1.60943791 \dots$