Solve for x 2 natural log of 3 = natural log of x-4

$2 \ln (3) = \ln (x - 4)$

Step 1

Rewrite the equation as $\ln (x - 4) = 2 \ln (3)$ .

$\ln (x - 4) = 2 \ln (3)$

Step 2

Simplify $2 \ln (3)$ by moving $2$ inside the logarithm.

$\ln (x - 4) = \ln (3^{2})$

Step 3

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$x - 4 = 3^{2}$

Step 4

Solve for $x$ .

Raise $3$ to the power of $2$ .

$x - 4 = 9$

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

Add $4$ to both sides of the equation.

$x = 9 + 4$

Add $9$ and $4$ .

$x = 13$