Solve for x natural log of 7=2x-2

$\ln (7) = 2 x - 2$

Rewrite the equation as $2 x - 2 = \ln (7)$ .

$2 x - 2 = \ln (7)$

Add $2$ to both sides of the equation.

$2 x = \ln (7) + 2$

Divide each term in $2 x = \ln (7) + 2$ by $2$ and simplify.

Divide each term in $2 x = \ln (7) + 2$ by $2$ .

$\frac{2 x}{2} = \frac{\ln (7)}{2} + \frac{2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{\ln (7)}{2} + \frac{2}{2}$

Divide $x$ by $1$ .

$x = \frac{\ln (7)}{2} + \frac{2}{2}$

Simplify the right side.

Simplify each term.

Rewrite $\frac{\ln (7)}{2}$ as $\frac{1}{2} \ln (7)$ .

$x = \frac{1}{2} \ln (7) + \frac{2}{2}$

Simplify $\frac{1}{2} \ln (7)$ by moving $\frac{1}{2}$ inside the logarithm.

$x = \ln (7^{\frac{1}{2}}) + \frac{2}{2}$

Divide $2$ by $2$ .

$x = \ln (7^{\frac{1}{2}}) + 1$

The result can be shown in multiple forms.

Exact Form:

$x = \ln (7^{\frac{1}{2}}) + 1$

Decimal Form:

$x = 1.97295507 \dots$