Solve for x e^x+1=7

$e^{x} + 1 = 7$

Step 1

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

Subtract $1$ from both sides of the equation.

$e^{x} = 7 - 1$

Subtract $1$ from $7$ .

$e^{x} = 6$

Step 2

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

$\ln (e^{x}) = \ln (6)$

Step 3

Expand the left side.

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

$x \ln (e) = \ln (6)$

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

$x \cdot 1 = \ln (6)$

Multiply $x$ by $1$ .

$x = \ln (6)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \ln (6)$

Decimal Form:

$x = 1.79175946 \dots$